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Signals, Volume 5, Issue 4 (December 2024) – 13 articles

Cover Story (view full-size image): Quasi-periodic signals, such as those in speech or music, can be modeled as harmonic sinusoids whose frequencies, magnitudes, and phases shape their waveforms. While frequency and magnitude estimation are well studied, accurate phase estimation has often been overlooked. By focusing on robust DFT-based techniques, this work shows how to estimate and model harmonic phases in a time-shift invariant manner, which not only provides fresh insights into the underlying generation mechanisms but also reveals a holistic harmonic phase structure that simplifies parametric modeling and enables flexible signal transformations. Performance results are discussed for six scenarios involving two DFT-based filter banks and three different windows. Reproducible examples and codes are provided, encouraging further exploration. View this paper
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14 pages, 6781 KiB  
Article
Identification of Vertebrae in CT Scans for Improved Clinical Outcomes Using Advanced Image Segmentation
by Sushmitha, M. Kanthi, Vishnumurthy Kedlaya K, Tejasvi Parupudi, Shyamasunder N. Bhat and Subramanya G. Nayak
Signals 2024, 5(4), 869-882; https://doi.org/10.3390/signals5040047 - 16 Dec 2024
Viewed by 613
Abstract
This study proposes a comprehensive framework for the segmentation and identification of vertebrae in CT scans using a combination of deep learning and traditional machine learning techniques. The Res U-Net architecture is employed to achieve a high model accuracy of 93.62% on the [...] Read more.
This study proposes a comprehensive framework for the segmentation and identification of vertebrae in CT scans using a combination of deep learning and traditional machine learning techniques. The Res U-Net architecture is employed to achieve a high model accuracy of 93.62% on the VerSe’20 dataset demonstrating effective performance in segmenting lumbar and thoracic vertebrae. Feature extraction is enhanced through the application of Otsu’s method which effectively distinguishes the vertebrae from the surrounding tissue. The proposed method achieves a Dice Similarity Coefficient (DSC) of 87.10% ± 3.72%, showcasing its competitive performance against other segmentation techniques. By accurately extracting vertebral features this framework assists medical professionals in precise preoperative planning, allowing for the identification and marking of critical anatomical features required during spinal fusion procedures. This integrated approach not only addresses the challenges of vertebrae segmentation but also offers a scalable and efficient solution for analyzing large-scale medical imaging datasets with the potential to significantly improve clinical workflows and patient outcomes. Full article
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Figure 1
<p>Segmentation of the vertebrae using Res U-Net.</p>
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<p>Architecture of the Res U-Net model for vertebrae segmentation. The model includes Convolutional Blocks (CA Blocks), Max-Pooling Layers for down-sampling, Up-Convolution Layers for up-sampling, and a Hierarchical Dense Aggregation (HDAC) Layer for efficient multi-scale feature aggregation. Input CT scans with a resolution of 512 × 512 pixels are processed through this network to generate segmented images.</p>
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<p>Training accuracy of the Res U-Net model over iterations for three datasets.</p>
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<p>Validation loss over epochs for three different datasets.</p>
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<p>Otsu’s feature extraction algorithm.</p>
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<p>Vertebra segmentation using Res U-Net (<b>a</b>) CT scan image (<b>b</b>) Ground truth (<b>c</b>) Segmented vertebrae.</p>
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<p>Vertebra feature extraction using Otsu’s method. (<b>a</b>) CT scan image (<b>b</b>). Segmented binary mask. (<b>c</b>) CT image with segmented contour.</p>
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<p>Final segmented 3D image of the vertebrae.</p>
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28 pages, 3162 KiB  
Article
Demystifying DFT-Based Harmonic Phase Estimation, Transformation, and Synthesis
by Marco Oliveira, Vasco Santos, André Saraiva and Aníbal Ferreira
Signals 2024, 5(4), 841-868; https://doi.org/10.3390/signals5040046 - 4 Dec 2024
Viewed by 998
Abstract
Many natural signals exhibit quasi-periodic behaviors and are conveniently modeled as combinations of several harmonic sinusoids whose relative frequencies, magnitudes, and phases vary with time. The waveform shapes of those signals reflect important physical phenomena underlying their generation, requiring those parameters to be [...] Read more.
Many natural signals exhibit quasi-periodic behaviors and are conveniently modeled as combinations of several harmonic sinusoids whose relative frequencies, magnitudes, and phases vary with time. The waveform shapes of those signals reflect important physical phenomena underlying their generation, requiring those parameters to be accurately estimated and modeled. In the literature, accurate phase estimation and modeling have received significantly less attention than frequency or magnitude estimation. This paper first addresses accurate DFT-based phase estimation of individual sinusoids across six scenarios involving two DFT-based filter banks and three different windows. It has been shown that bias in phase estimation is less than 0.001 radians when the SNR is equal to or larger than 2.5 dB. Using the Cramér–Rao lower bound as a reference, it has been demonstrated that one particular window offers performance of practical interest by better approximating the CRLB under favorable signal conditions and minimizing performance deviation under adverse conditions. This paper describes the development of a shift-invariant phase-related feature that characterizes the harmonic phase structure. This feature motivates a new signal processing paradigm that greatly simplifies the parametric modeling, transformation, and synthesis of harmonic signals. It also aids in understanding and reverse engineering the phasegram. The theory and results are discussed from a reproducible perspective, with dedicated experiments supported by code, allowing for the replication of figures and results presented in this paper and facilitating further research. Full article
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Graphical abstract

Graphical abstract
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<p>In many harmonic signal processing applications, individual harmonics are processed separately. Signal modification converts the original fundamental frequency (<math display="inline"><semantics> <msub> <mi>ω</mi> <mn>0</mn> </msub> </semantics></math>), the original harmonic magnitudes (<math display="inline"><semantics> <msub> <mi>A</mi> <mo>ℓ</mo> </msub> </semantics></math>), and phases (<math display="inline"><semantics> <msub> <mi>ϕ</mi> <mo>ℓ</mo> </msub> </semantics></math>), into new values (<math display="inline"><semantics> <msubsup> <mi>ω</mi> <mrow> <mn>0</mn> </mrow> <mi>S</mi> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>A</mi> <mrow> <mo>ℓ</mo> </mrow> <mi>S</mi> </msubsup> </semantics></math>, <math display="inline"><semantics> <msubsup> <mi>ϕ</mi> <mrow> <mo>ℓ</mo> </mrow> <mi>S</mi> </msubsup> </semantics></math>) in the synthesis process.</p>
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<p>A convenient paradigm in harmonic signal processing: a holistic harmonic magnitude and phase structure represented by a shift-invariant and fundamental frequency-independent magnitude model (MM), and phase model (PM), respectively. Signal transformation just involves modifications to these models.</p>
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<p>Normalized magnitude of the frequency response of the rectangular, sine, and Hanning windows in the range <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>8</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> <mo>≤</mo> <mi>ω</mi> <mo>≤</mo> <mn>8</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> </mrow> </semantics></math>. The frequency axis (<math display="inline"><semantics> <mi>ω</mi> </semantics></math>) is normalized by <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>π</mi> <mo>/</mo> <mi>N</mi> </mrow> </semantics></math>.</p>
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<p>When <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mo>−</mo> <mn>0.5</mn> <mo>,</mo> <mn>0.5</mn> <mo>[</mo> </mrow> </mrow> </semantics></math>, the magnitude spectrum of the DFT of a rectangular-windowed sinusoid exhibits a local maximum for <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <msub> <mi>k</mi> <mo>ℓ</mo> </msub> </mrow> </semantics></math>. The plots illustrate the case when <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> <mo>=</mo> <mo>−</mo> <mn>0.5</mn> <mo>+</mo> <mi>ϵ</mi> </mrow> </semantics></math> (<b>left</b>), when <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math> (<b>center</b>), and when <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> <mo>=</mo> <mn>0.5</mn> <mo>−</mo> <mi>ϵ</mi> </mrow> </semantics></math> (<b>right</b>), where <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>&lt;</mo> <mn>0.5</mn> </mrow> </semantics></math> is a small real positive number.</p>
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<p>Cumulative phase estimation error as a function of the fractional frequency <math display="inline"><semantics> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> </semantics></math>, when the DFT and the rectangular window are used. In the illustrated cases, <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math>, SNR = 30 dB (<b>left</b>) and SNR = 10 dB (<b>right</b>).</p>
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<p>When <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mo>−</mo> <mn>0.5</mn> <mo>,</mo> <mn>0.5</mn> <mo>]</mo> </mrow> </mrow> </semantics></math>, the magnitude spectrum of the DFT of a sine-windowed sinusoid exhibits a local maximum for <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <msub> <mi>k</mi> <mo>ℓ</mo> </msub> </mrow> </semantics></math>. The plots illustrate the case when <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> <mo>=</mo> <mo>−</mo> <mn>0.5</mn> <mo>+</mo> <mi>ϵ</mi> </mrow> </semantics></math> (<b>left</b>), when <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math> (<b>center</b>), and when <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> <mo>=</mo> <mn>0.5</mn> <mo>−</mo> <mi>ϵ</mi> </mrow> </semantics></math> (<b>right</b>), where <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>&lt;</mo> <mn>0.5</mn> </mrow> </semantics></math> is a small real positive number.</p>
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<p>Cumulative phase estimation error as a function of the fractional frequency <math display="inline"><semantics> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> </semantics></math>, when the DFT and the sine window are used. In the illustrated cases, <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math>, SNR = 30 dB (<b>left</b>) and SNR = 10 dB (<b>right</b>).</p>
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<p>Cumulative phase estimation error as a function of the fractional frequency <math display="inline"><semantics> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> </semantics></math>, when the ODFT and the rectangular window are used. In the illustrated cases, <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math>, SNR = 30 dB (<b>left</b>) and SNR = 10 dB (<b>right</b>).</p>
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<p>Cumulative phase estimation error as a function of the fractional frequency <math display="inline"><semantics> <msub> <mo>Δ</mo> <mo>ℓ</mo> </msub> </semantics></math>, when the ODFT and the sine window are used. In the illustrated cases, <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math>, SNR = 30 dB (<b>left</b>) and SNR = 10 dB (<b>right</b>).</p>
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<p>Mean over 100 Monte Carlo runs of the phase estimation error when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math>, and when <math display="inline"><semantics> <mo>Δ</mo> </semantics></math> takes on two extreme values depending on the estimator.</p>
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<p>Variance of the phase estimation error when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math>, and when <math display="inline"><semantics> <mo>Δ</mo> </semantics></math> takes on two extreme values depending on the estimator. The Cramér–Rao lower bound is also represented although it is not too visible since it is overlapped by the DFT-RECT results when <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math>.</p>
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<p>An inspiring metaphor from nature: NRD can be regarded as being similar to the space-invariant bird formation structure in a flock that is represented by the line connecting the birds in the upper branch of the illustrated flock.</p>
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<p>Two FM deviation cases characterizing test signals: FM = 2.5 Hz (solid line) and FM = 0.25 Hz (dashed line).</p>
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<p>Illustration of the influence of noise on the sawtooth test signal when SNR = 30 dB (<b>top</b>), and when SNR = 10 dB (<b>bottom</b>).</p>
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<p>Overlay representation of magnitude spectra (<b>top</b>), and unwrapped NRD vectors (<b>bottom</b>) of a sawtooth signal that is FM modulated (0.25 Hz deviation around the mean) and whose SNR is 30 dB.</p>
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<p>Overlay representation of magnitude spectra (<b>top</b>), and unwrapped NRD vectors (<b>bottom</b>) of a sawtooth signal that is FM modulated (0.25 Hz deviation around the mean) and whose SNR is 10 dB.</p>
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<p>Overlay representation of magnitude spectra (<b>top</b>), and unwrapped NRD vectors (<b>bottom</b>) of a sawtooth signal that is FM modulated (2.5 Hz deviation around the mean) and whose SNR is 30 dB.</p>
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<p>Overlay representation of magnitude spectra (<b>top</b>), and unwrapped NRD vectors (<b>bottom</b>) of a sawtooth signal that is FM modulated (2.5 Hz deviation around the mean) and whose SNR is 10 dB.</p>
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<p>Illustration of the derivative of the sawtooth test signal when it is affected by noise at SNR = 30 dB (<b>top</b>), and at SNR = 10 dB (<b>bottom</b>).</p>
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<p>Overlay representation of magnitude spectra (<b>top</b>), and unwrapped NRD vectors (<b>bottom</b>) of a sawtooth derivative signal that is FM-modulated (2.5 Hz deviation around the mean) and whose SNR is 30 dB.</p>
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<p>Overlay representation of magnitude spectra (<b>top</b>), and unwrapped NRD vectors (<b>bottom</b>) of the negative of a sawtooth derivative signal that is FM modulated (2.5 Hz deviation around the mean) and whose SNR is 30 dB.</p>
Full article ">Figure 22
<p>Overlay representation of magnitude spectra (<b>top</b>), and unwrapped NRD vectors (<b>bottom</b>) of a sawtooth derivative signal that is FM modulated (2.5 Hz deviation around the mean) and whose SNR is 10 dB.</p>
Full article ">Figure 23
<p>Overlay representation of magnitude spectra (<b>top</b>), and unwrapped NRD vectors (<b>bottom</b>) of the negative of a sawtooth derivative signal that is FM modulated (2.5 Hz deviation around the mean) and whose SNR is 10 dB.</p>
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<p>Example of a harmonic phase model (<b>a</b>) and harmonic magnitude model (<b>b</b>) pertaining to a female sustained vowel signal.</p>
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<p>Example of a harmonic phase model (<b>a</b>) and harmonic magnitude model (<b>b</b>) pertaining to a male sustained vowel signal.</p>
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<p>Spectrogram (<b>a</b>), phasegram (<b>b</b>), and synthetic phasegram (<b>c</b>) characterizing the first 4 harmonics of a sawtooth waveform.</p>
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29 pages, 2345 KiB  
Article
Signal Processing for Transient Flow Rate Determination: An Analytical Soft Sensor Using Two Pressure Signals
by Faras Brumand-Poor, Tim Kotte, Enrico Gaspare Pasquini and Katharina Schmitz
Signals 2024, 5(4), 812-840; https://doi.org/10.3390/signals5040045 - 2 Dec 2024
Viewed by 712
Abstract
Accurate knowledge of the flow rate is essential for hydraulic systems, enabling the calculation of hydraulic power when combined with pressure measurements. These data are crucial for applications such as predictive maintenance. However, most flow rate sensors in fluid power systems operate invasively, [...] Read more.
Accurate knowledge of the flow rate is essential for hydraulic systems, enabling the calculation of hydraulic power when combined with pressure measurements. These data are crucial for applications such as predictive maintenance. However, most flow rate sensors in fluid power systems operate invasively, disrupting the flow and producing inaccurate results, especially under transient conditions. Utilizing pressure transducers represents a non-invasive soft sensor approach since no physical flow rate sensor is used to determine the flow rate. Usually, this approach relies on the Hagen–Poiseuille (HP) law, which is limited to steady and incompressible flow. This paper introduces a novel soft sensor with an analytical model for transient, compressible pipe flow based on two pressure signals. The model is derived by solving fundamental fluid equations in the Laplace domain and converting them back to the time domain. Using the four-pole theorem, this model contains a relationship between the pressure difference and the flow rate. Several unsteady test cases are investigated and compared to a steady soft sensor based on the HP law, highlighting our soft sensor’s promising capability. It exhibits an overall error of less than 0.15% for the investigated test cases in a distributed-parameter simulation, whereas the HP-based sensor shows errors in the double-digit range. Full article
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Graphical abstract

Graphical abstract
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<p>Laminar velocity profiles for various Womersley numbers ranging from 1.5 to 30 with a phase angle of 90° (right side) and laminar velocity profiles for various phase angles ranging from 90° to 190° with a Womersley number of 30.</p>
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<p>Flowchart of the derivation of the soft sensor equations.</p>
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<p>Logarithm of absolute of weighting function <math display="inline"><semantics> <msubsup> <mi>W</mi> <mn>1</mn> <mo>*</mo> </msubsup> </semantics></math> for real and imaginary arguments for fixed dissipation number.</p>
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<p>Weighting functions featuring only residues of negative real poles (incompressible solution) and residues of all poles (compressible solution).</p>
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<p>Weighting functions featuring only residues of negative real poles (incompressible solution) and residues of all poles (compressible solution).</p>
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<p>ILT using residue theorem for both weighting functions.</p>
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<p>Position of the poles of <math display="inline"><semantics> <mrow> <msubsup> <mi>W</mi> <mrow> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>ζ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for various <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>n</mi> </mrow> </semantics></math>.</p>
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<p>The 1 Hz sine wave pressure boundary at the 50 bar level.</p>
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<p>The 100 Hz sine wave pressure boundary at the 50 bar level.</p>
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<p>The 1000 Hz sine wave pressure boundary at the 50 bar level.</p>
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<p>Sum of sine waves with 1 Hz, 10 Hz, 20 Hz, and 40 Hz pressure boundaries at 50 bar level.</p>
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<p>Sum of sine waves with 10 Hz, 100 Hz, 200 Hz, and 400 Hz pressure boundaries at 50 bar level.</p>
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<p>Sawtooth pressure boundary at 50 bar level.</p>
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<p>Step function pressure boundary at 50 bar level.</p>
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18 pages, 1534 KiB  
Article
RIP Sensing Matrices Construction for Sparsifying Dictionaries with Application to MRI Imaging
by Jinn Ho, Wen-Liang Hwang and Andreas Heinecke
Signals 2024, 5(4), 794-811; https://doi.org/10.3390/signals5040044 - 2 Dec 2024
Viewed by 505
Abstract
Practical applications of compressed sensing often restrict the choice of its two main ingredients. They may (i) prescribe the use of particular redundant dictionaries for certain classes of signals to become sparsely represented or (ii) dictate specific measurement mechanisms which exploit certain physical [...] Read more.
Practical applications of compressed sensing often restrict the choice of its two main ingredients. They may (i) prescribe the use of particular redundant dictionaries for certain classes of signals to become sparsely represented or (ii) dictate specific measurement mechanisms which exploit certain physical principles. On the problem of RIP measurement matrix design in compressed sensing with redundant dictionaries, we give a simple construction to derive sensing matrices whose compositions with a prescribed dictionary have with high probability the RIP in the klog(n/k) regime. Our construction thus provides recovery guarantees usually only attainable for sensing matrices from random ensembles with sparsifying orthonormal bases. Moreover, we use the dictionary factorization idea that our construction rests on in the application of magnetic resonance imaging, in which also the sensing matrix is prescribed by quantum mechanical principles. We propose a recovery algorithm based on transforming the acquired measurements such that the compressed sensing theory for RIP embeddings can be utilized to recover wavelet coefficients of the target image, and show its performance on examples from the fastMRI dataset. Full article
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Figure 1

Figure 1
<p>Visualization of sparsifying dictionaries (of size <math display="inline"><semantics> <mrow> <mn>128</mn> <mo>×</mo> <mn>1024</mn> </mrow> </semantics></math>) with integer values ranging from 0 to 255.</p>
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<p>Matrix <math display="inline"><semantics> <mrow> <mi>G</mi> <mo>∈</mo> <msup> <mi mathvariant="double-struck">R</mi> <mrow> <mn>128</mn> <mo>×</mo> <mn>128</mn> </mrow> </msup> </mrow> </semantics></math> of several sparsifying dictionaries <span class="html-italic">D</span> for various <span class="html-italic">A</span>. Recall that <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mi>G</mi> <mi>A</mi> <mi>H</mi> </mrow> </semantics></math> and the sensing matrix of <span class="html-italic">D</span> is <math display="inline"><semantics> <mrow> <mi mathvariant="script">E</mi> <msup> <mi>G</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>. In (<b>a1</b>,<b>b1</b>), <span class="html-italic">A</span> is a Gaussian random matrix. In (<b>a2</b>,<b>b2</b>), <span class="html-italic">A</span> is a Bernoulli random matrix. In (<b>a1</b>,<b>a2</b>), <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <msub> <mi>D</mi> <mrow> <mi>K</mi> <mi>S</mi> <mi>V</mi> <mi>D</mi> </mrow> </msub> </mrow> </semantics></math>. In (<b>b1</b>,<b>b2</b>), <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <msub> <mi>D</mi> <mrow> <mi>w</mi> <mi>a</mi> <mi>v</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Comparisons of CS recovery performance (i.e., the probability of sparse vector recovery versus CS ratio) using sparsifying dictionary <math display="inline"><semantics> <msub> <mi>D</mi> <mrow> <mi>K</mi> <mi>S</mi> <mi>V</mi> <mi>D</mi> </mrow> </msub> </semantics></math>. Red and blue curves were, respectively, obtained using the benchmark (<a href="#FD12-signals-05-00044" class="html-disp-formula">12</a>) and our approach (<a href="#FD11-signals-05-00044" class="html-disp-formula">11</a>). Sparse vectors <span class="html-italic">x</span> were randomly generated and each point on the curve is the average of 2000 probability measurements. The positions of non-zero coefficients of <span class="html-italic">x</span> are uniformly distributed and the values of the non-zero coefficients of <span class="html-italic">x</span> are uniformly distributed in <math display="inline"><semantics> <mrow> <mo>[</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics></math>. In (<b>a1</b>,<b>a2</b>), sparsity level is 10; in (<b>b1</b>,<b>b2</b>), sparsity level is 12; and in (<b>c1</b>,<b>c2</b>), sparsity level is 14.</p>
Full article ">Figure 4
<p>Comparisons of CS recovery performance (i.e., the probability of sparse vector recovery versus CS ratio) using sparsifying dictionary <math display="inline"><semantics> <msub> <mi>D</mi> <mrow> <mi>w</mi> <mi>a</mi> <mi>v</mi> <mi>e</mi> <mi>l</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </semantics></math> (CDF 9/7). Red and blue curves were, respectively, obtained using the benchmark (<a href="#FD12-signals-05-00044" class="html-disp-formula">12</a>) and our approach (<a href="#FD11-signals-05-00044" class="html-disp-formula">11</a>). Sparse vectors <span class="html-italic">x</span> were randomly generated and each point on the curve is the average of 2000 probability measurements. The positions of non-zero coefficients of <span class="html-italic">x</span> are uniformly distributed and the values of the non-zero coefficients of <span class="html-italic">x</span> are uniformly distributed in <math display="inline"><semantics> <mrow> <mo>[</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics></math>. In (<b>a1</b>,<b>a2</b>), sparsity level is 10; in (<b>b1</b>,<b>b2</b>), sparsity level is 12; and in (<b>c1</b>,<b>c2</b>), sparsity level is 14.</p>
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<p>Scan line locations for 4-fold (<b>left</b>) and 8-fold (<b>right</b>) under-sampling, including fully sampled low-frequency region.</p>
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<p>(<b>a0</b>) FFT reconstruction of fully sampled MRI <span class="html-italic">k</span>-space data (file 1000031.h5: the 20th in a set of 40 datasets, each comprising <math display="inline"><semantics> <mrow> <mn>372</mn> <mo>×</mo> <mn>640</mn> </mrow> </semantics></math> data points, representing coronal proton density (PD) knee images). (<b>a1</b>) Image of the proposed algorithm with 4-fold sampling. (<b>a2</b>) Image of the proposed algorithm with 8-fold sampling. (<b>b1</b>) Image of the TV algorithm with 4-fold sampling. (<b>b2</b>) Image of the TV algorithm with 8-fold sampling. The vertical band patterns observed in the images are artifacts resulting from under-sampling. The artifact in (<b>a2</b>) is less noticeable compared to (<b>b2</b>).</p>
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<p>(<b>a0</b>) FFT reconstruction of fully sampled MRI <span class="html-italic">k</span>-space data (file 1000071.h5: the 20th in a set of 35 datasets, each comprising <math display="inline"><semantics> <mrow> <mn>372</mn> <mo>×</mo> <mn>640</mn> </mrow> </semantics></math> data points, representing coronal proton density (PD) knee images). (<b>a1</b>) Image of the proposed algorithm with 4-fold sampling. (<b>a2</b>) Image of the proposed algorithm with 8-fold sampling. (<b>b1</b>) Image of the TV algorithm with 4-fold sampling. (<b>b2</b>) Image of the TV algorithm with 8-fold sampling.</p>
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<p>(<b>a0</b>) The fully sampled MRI <span class="html-italic">k</span>-space data (file_brain_AXT1_201_6002786.h5) involves the second set of 16 brain datasets, each containing <math display="inline"><semantics> <mrow> <mn>320</mn> <mo>×</mo> <mn>640</mn> </mrow> </semantics></math> data points. (<b>a1</b>) Image displaying the proposed algorithm with 4-fold sampling. (<b>a2</b>) Image displaying the proposed algorithm with 8-fold sampling. (<b>b1</b>) Image showing the TV algorithm with 4-fold sampling. (<b>b2</b>) Image showing the TV algorithm with 8-fold sampling. The structure is more discernible in (<b>a2</b>) and (<b>a1</b>) than in (<b>b2</b>) and (<b>b1</b>), respectively.</p>
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<p>(<b>a0</b>) The fully sampled MRI <span class="html-italic">k</span>-space data (file_brain_AXT1_201_6002740.h5) involves the second set of 16 brain datasets, each containing <math display="inline"><semantics> <mrow> <mn>320</mn> <mo>×</mo> <mn>640</mn> </mrow> </semantics></math> data points. (<b>a1</b>) Image displaying the proposed algorithm with 4-fold sampling. (<b>a2</b>) Image displaying the proposed algorithm with 8-fold sampling. (<b>b1</b>) Image showing the TV algorithm with 4-fold sampling. (<b>b2</b>) Image showing the TV algorithm with 8-fold sampling. The structure is more discernible in (<b>a2</b>) and (<b>a1</b>) than in (<b>b2</b>) and (<b>b1</b>), respectively.</p>
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20 pages, 10700 KiB  
Article
A 2.4 GHz IEEE 802.15.4 Multi-Hop Network for Mountainous Forest and Watercourse Environments: Sensor Node Deployment and Performance Evaluation
by Apidet Booranawong, Puwasit Hirunkitrangsri, Dujdow Buranapanichkit, Charernkiat Pochaiya, Nattha Jindapetch and Hiroshi Saito
Signals 2024, 5(4), 774-793; https://doi.org/10.3390/signals5040043 - 20 Nov 2024
Viewed by 708
Abstract
In this paper, we demonstrate the realistic test of a 2.4 GHz multi-hop wireless network for mountainous forest and watercourse environments. A multi-hop network using IEEE 802.15.4 XBee3 micro-modules and a communication protocol among nodes were developed. A wireless node deployment solution was [...] Read more.
In this paper, we demonstrate the realistic test of a 2.4 GHz multi-hop wireless network for mountainous forest and watercourse environments. A multi-hop network using IEEE 802.15.4 XBee3 micro-modules and a communication protocol among nodes were developed. A wireless node deployment solution was introduced for practical testing. The proposed system’s communication reliability was tested in two different scenarios: a mountainous forest with sloping areas and trees and a watercourse, which referred to environmental and flooding monitoring applications. Wireless network performances were evaluated through the received signal strength indicator (RSSI) level of each wireless link, a packet delivery ratio (PDR), as the successful rate of packet transmission, and the end-to-end delay (ETED) of all data packets from the transmitter to the receiver. The experimental results demonstrate the success of the multi-hop WSN deployment and communication in both scenarios, where the RSSI of each link was kept at the accepted level and the PDR achieved the highest result. Furthermore, as a real-time response, the data from the source could be sent to the sink with a small ETED. Full article
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<p>A multi-hop WSN with the communication protocol among the nodes.</p>
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<p>Example of the proposed sensor node deployment process (before the data collection phase.</p>
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<p>Example of the proposed sensor node deployment process (before the data collection phase.</p>
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<p>Example of the proposed sensor node deployment process (before the data collection phase.</p>
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<p>Test scenarios #1 and #2.</p>
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<p>The test field layouts.</p>
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<p>Illustration of sensor node deployment and environments.</p>
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<p>An example of water flooding during the rainy season for field #2.</p>
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<p>Examples of raw RSSI signals collected from test scenario #1 (test times 5 and 15). The signals could be displayed in real time during the test in the GUI window. Note that the y-axis is the RSSI level in dBm, and RSSI B, C, and D refer to hops 3, 2, and 1.</p>
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<p>Average RSSIs of hops 1 to 3 for test scenarios #1 and #2.</p>
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<p>PDR results.</p>
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<p>ETED results.</p>
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<p>ETED results.</p>
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<p>The XBee3 micro-module with the GY-521 accelerometer/gyro sensor and 5 V battery.</p>
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<p>Examples of three-axis acceleration and gyro signals.</p>
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<p>Examples of three-axis acceleration and gyro signals.</p>
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<p>Examples of three-axis acceleration and gyro signals.</p>
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18 pages, 4090 KiB  
Review
Fusion of Telecommunications and IT Services Boosted by Application Programming Interfaces
by Máté Ákos Tündik, Zsolt Szabó, Attila Hilt and Gábor Járó
Signals 2024, 5(4), 756-773; https://doi.org/10.3390/signals5040042 - 12 Nov 2024
Viewed by 1070
Abstract
Our long journey on the road of telecommunications is continuously evolving. We have experienced several technological changes, modernizations, optimizations, and various mergers in the past decades. Virtualization and ‘cloudification’ of legacy telecommunication equipment has made communication networks not only more flexible, but also [...] Read more.
Our long journey on the road of telecommunications is continuously evolving. We have experienced several technological changes, modernizations, optimizations, and various mergers in the past decades. Virtualization and ‘cloudification’ of legacy telecommunication equipment has made communication networks not only more flexible, but also opened new doors. Brand new types of services have become available thanks to the ongoing fusion of the two domains of telecommunications and IT (Information Technology). This overview paper first discusses the evolution of services with an enhanced focus on mobile networks. Then, the possibilities offered by IT are shown. Finally, some examples are given of how Communication Service Providers and end users can benefit from these recent changes. Full article
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<p>The evolving telecommunication network as a mesh of various fixed and mobile access technologies and core networks.</p>
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<p>General IN architecture with decoupled business and service logic [<a href="#B36-signals-05-00042" class="html-bibr">36</a>].</p>
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<p>2G/3G mobile service logic over CAMEL with decoupled business and service logic [<a href="#B36-signals-05-00042" class="html-bibr">36</a>].</p>
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<p>Alternatives to provide CS domain services in the IMS domain (<b>A</b>: continue with the existing IN service, <b>B</b>: implement the service natively as an IMS AS, <b>C</b>: invoke the service over API).</p>
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<p>Traditional IN-based services executed by the IM-SSF.</p>
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<p>Application programming interface-based solution in Nokia Telephony Application Server.</p>
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<p>Fusion of IT and telco worlds.</p>
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<p>Use cases after IT–Telco fusions.</p>
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<p>Convergence of telco services.</p>
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20 pages, 8075 KiB  
Article
Comparative Analysis of Statistical, Time–Frequency, and SVM Techniques for Change Detection in Nonlinear Biomedical Signals
by Tahmineh Azizi
Signals 2024, 5(4), 736-755; https://doi.org/10.3390/signals5040041 - 7 Nov 2024
Viewed by 748
Abstract
Change detection in biomedical signals is crucial for understanding physiological processes and diagnosing medical conditions. This study evaluates various change detection methods, focusing on synthetic signals that mimic real-world scenarios. We examine the following three methods: classical statistical techniques (thresholding based on mean [...] Read more.
Change detection in biomedical signals is crucial for understanding physiological processes and diagnosing medical conditions. This study evaluates various change detection methods, focusing on synthetic signals that mimic real-world scenarios. We examine the following three methods: classical statistical techniques (thresholding based on mean and standard deviation), Support Vector Machine (SVM) classification, and time–frequency analysis using Continuous Wavelet Transform (CWT). Each method’s performance is assessed using synthetic signals, including nonlinear signals and those with simulated anomalies. We calculated the F1-score to quantify performance, providing a balanced measure of precision and recall. Results showed that SVM classification outperformed both classical techniques and CWT analysis, achieving a higher F1-score in detecting changes. While all methods struggled with synthetic nonlinear signals, classical techniques and SVM successfully detected changes in signals with simulated anomalies, whereas CWT had difficulty with both types of signals. These findings underscore the importance of selecting appropriate change detection methods based on signal characteristics. Future research should explore advanced machine learning and signal processing techniques to improve detection accuracy in biomedical applications. Full article
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<p>Change detection in biomedical signals. This figure illustrates the performance of different change detection methods on a synthetic signal. The original signal contains a known anomaly between time points 100 and 150. The classical statistical method uses mean and standard deviation thresholding to identify changes. The Continuous Wavelet Transform (CWT) method analyzes the signal in both time and frequency domains to detect anomalies. The Support Vector Machine (SVM) classifier is trained on the signal to identify changes based on learned patterns. The figure highlights the detected anomalies by each method, demonstrating their effectiveness in identifying different types of changes in biomedical signals.</p>
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<p>Support Vector Machine (SVM) workflow. An SVM classifies data by finding the optimal hyperplane that separates two classes with maximum margin. Kernel functions map data into a higher-dimensional space to improve separability. The soft margin approach allows for some misclassification, balancing accuracy and generalization. The kernel trick efficiently computes dot products in the transformed space. The SVM training process involves solving a convex optimization problem to learn the hyperplane parameters. Once trained, the SVM can predict class labels for new data points based on their distance from the hyperplane.</p>
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<p>Schematic representation of change detection methods applied to a biomedical signal. The original biomedical signal (blue curve) is analyzed using three methods: classical statistical techniques, Continuous Wavelet Transform (CWT), and Support Vector Machine (SVM). Changes detected by the statistical method are highlighted in the red shaded area, indicating sensitivity to shifts in mean and standard deviation. Changes identified by the CWT method are shown in the green shaded area, demonstrating the method’s ability to capture time–frequency variations. The SVM-detected changes are marked by black arrows, showcasing its capability to recognize subtle and complex patterns in the signal. This visualization underscores the varying effectiveness of each method in different contexts of signal complexity and change characteristics.</p>
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<p>Change detection using mean and standard deviation method. (<b>Top</b>) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations and fluctuations in amplitude. (<b>Bottom</b>) The red line represents the results of change detection using the mean and standard deviation method.</p>
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<p>Change detection using mean and standard deviation method. (<b>Top</b>) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations and fluctuations in amplitude. (<b>Bottom</b>) The red line represents the results of change detection using the mean and standard deviation method.</p>
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<p>Change detection using Wavelet Transform. (<b>Top</b>) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations and fluctuations in amplitude. (<b>Bottom</b>) The bottom subplot displays the results of change detection using the Wavelet Transform method. Changes in the signal are represented by localized regions of high wavelet coefficients, indicating deviations from the background signal.</p>
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<p>Change detection using Wavelet Transform. (<b>Top</b>) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations and fluctuations in amplitude. (<b>Bottom</b>) The bottom subplot displays the results of change detection using the Wavelet Transform method. Changes in the signal are represented by localized regions of high wavelet coefficients, indicating deviations from the background signal.</p>
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<p>Change detection in synthetic signal using Support Vector Machine (SVM) classification. (<b>Top</b>) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations and fluctuations in amplitude. (<b>Bottom</b>) Change detection results using Support Vector Machine (SVM) classifier, where red indicates predicted change points based on the trained model.</p>
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<p>Change detection in synthetic signal using Support Vector Machine (SVM) classification. (<b>Top</b>) Synthetic signal with a sinusoidal pattern over a duration of 5 s. Random changes have been introduced into the signal to simulate anomalies, indicated by the red markers. These changes represent potential abnormalities or deviations from the expected signal pattern. (<b>Bottom</b>) The green line represents the true labels indicating the presence of changes in the signal, while the red dashed line represents the predicted labels obtained using a Support Vector Machine (SVM) classifier.</p>
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<p>Change detection in synthetic signal using Support Vector Machine (SVM) classification. (<b>Top</b>) Synthetic signal with complex patterns and amplitude spikes indicating changes (highlighted in red). (<b>Bottom</b>) Detected changes indicated by green (true labels) and red dashed lines (predicted labels) using SVM classification. The accuracy of change detection is shown in the title.</p>
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<p>Analysis of synthetic EEG signal and change detection. (<b>Top</b>) Mean and standard deviation of EEG signal: This subplot displays the mean (red dashed line) and one standard deviation above and below the mean (black dashed lines) of the generated EEG signal over time. The underlying blue line represents the raw EEG-like time series data, showcasing the variations around the average signal level. (<b>Middle</b>) Time–Frequency analysis (Spectrogram): The spectrogram in this subplot illustrates the time–frequency representation of the EEG signal using the short-time Fourier transform (STFT). The x-axis denotes time (in seconds), while the y-axis represents frequency (in Hz). The color intensity indicates the magnitude of the frequency components in decibels (dB), revealing the distribution of power across different frequency bands over time. (<b>Bottom</b>) SVM change detection: This subplot depicts the predicted labels for the EEG signal using a Support Vector Machine (SVM) model. The green line indicates detected changes across the time series, with ‘1’ representing no spike and ‘2’ indicating spike events. The visualization helps demonstrate the effectiveness of the SVM algorithm in identifying significant changes (spikes) in the EEG data.</p>
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<p>Analysis of synthetic sine wave signal and change detection. (<b>Top</b>) Original synthetic sine wave signal with a base frequency of 1 Hz (in blue), along with calculated mean (in green) and standard deviation (in red) lines. The abrupt changes in amplitude are highlighted in the signal plot between the vertical dashed lines. (<b>Middle</b>) Time–Frequency representation of the synthetic sine wave signal obtained via short-time Fourier transform (STFT). The spectrogram illustrates the frequency content over time, showing how the signal’s energy distribution shifts during the introduced changes. (<b>Bottom</b>) Change detection using Support Vector Machine (SVM) classification. The colored regions indicate the predicted states of the signal (baseline vs. changed amplitude), demonstrating the SVM’s ability to identify segments with different characteristics. The SVM was trained using features (mean and standard deviation) extracted from the signal.</p>
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15 pages, 13201 KiB  
Article
Quantifying Shape and Texture Biases for Enhancing Transfer Learning in Convolutional Neural Networks
by Akinori Iwata and Masahiro Okuda
Signals 2024, 5(4), 721-735; https://doi.org/10.3390/signals5040040 - 4 Nov 2024
Viewed by 836
Abstract
Neural networks have inductive biases owing to the assumptions associated with the selected learning algorithm, datasets, and network structure. Specifically, convolutional neural networks (CNNs) are known for their tendency to exhibit textural biases. This bias is closely related to image classification accuracy. Aligning [...] Read more.
Neural networks have inductive biases owing to the assumptions associated with the selected learning algorithm, datasets, and network structure. Specifically, convolutional neural networks (CNNs) are known for their tendency to exhibit textural biases. This bias is closely related to image classification accuracy. Aligning the model’s bias with the dataset’s bias can significantly enhance performance in transfer learning, leading to more efficient learning. This study aims to quantitatively demonstrate that increasing shape bias within the network by varying kernel sizes and dilation rates improves accuracy on shape-dominant data and enables efficient learning with less data. Furthermore, we propose a novel method for quantitatively evaluating the balance between texture bias and shape bias. This method enables efficient learning by aligning the biases of the transfer learning dataset with those of the model. Systematically adjusting these biases allows CNNs to better fit data with specific biases. Compared to the original model, an accuracy improvement of up to 9.9% was observed. Our findings underscore the critical role of bias adjustment in CNN design, contributing to developing more efficient and effective image classification models. Full article
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<p>The combined shape/texture images used to calculate the bias metric (on the left side) included a shape-dominant image in the upper part and a texture-dominant image in the lower part. This combined image is used for transfer learning in a two-class classification. Subsequently, these test-combined images are input into the model, and the shape/texture bias is calculated through gradient-weighted class activation mapping (Grad-CAM).</p>
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<p>Results of Grad-CAM visualization used with the proposed shape/texture bias metric. In the case of the original ResNeXt (a texture-biased model), the heat map of the lower image (which is texture-dominant) turns red, indicating that the model is focusing on it. On the other hand, for the ResNeXt with a dilation rate of three (a shape-biased model), the heat map of the upper image (which is shape-dominant) turns red, indicating its focus. This demonstrates that simply increasing the dilation rate results in a stronger bias towards shapes in the model. (<b>a</b>) The visualization images were obtained by applying Grad-CAM to the original ResNeXt (texture-biased model). (<b>b</b>) The visualization images were obtained by applying Grad-CAM to ResNeXt with a dilation of three (shape-biased model).</p>
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<p>Results of limiting the training data for each dataset. The accuracy rate is defined as the accuracy achieved with limited training data divided by the accuracy achieved with the entire dataset. The data ratio represents the proportion of the data used for training. (<b>a</b>) Results of reducing the amount of training data in the Logo dataset. (<b>b</b>) Results of reducing the amount of training data in the Cartoon dataset. (<b>c</b>) Results of reducing the amount of training data in the Sketch dataset.</p>
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<p>Results of limiting the training data for each dataset. The accuracy rate is defined as the accuracy achieved with limited training data divided by the accuracy achieved with the entire dataset. The data ratio represents the proportion of the data used for training. (<b>a</b>) Results of reducing the amount of training data in the Logo dataset. (<b>b</b>) Results of reducing the amount of training data in the Cartoon dataset. (<b>c</b>) Results of reducing the amount of training data in the Sketch dataset.</p>
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16 pages, 2500 KiB  
Article
Curved Text Line Rectification via Bresenham’s Algorithm and Generalized Additive Models
by Thomas Stogiannopoulos and Ilias Theodorakopoulos
Signals 2024, 5(4), 705-720; https://doi.org/10.3390/signals5040039 - 24 Oct 2024
Viewed by 878
Abstract
This paper presents a methodology for rectifying curved text lines, a crucial process in optical character recognition (OCR) and computer vision. Utilizing generalized additive models (GAMs), the proposed method accurately estimates text curvature and rectifies it into a straight format for improved text [...] Read more.
This paper presents a methodology for rectifying curved text lines, a crucial process in optical character recognition (OCR) and computer vision. Utilizing generalized additive models (GAMs), the proposed method accurately estimates text curvature and rectifies it into a straight format for improved text recognition. The process includes image binarization techniques like Otsu’s thresholding, morphological operations, curve estimation, and the Bresenham line drawing algorithm. The results show significant improvements in OCR accuracy among different challenging distortion scenarios. The implementation, written in Python, demonstrates the potential for enhancing text alignment and rectification in scanned text line images utilizing a flexible, robust, and customizable framework. Full article
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<p>An example demonstrating the outcome of Bresenham’s line algorithm [<a href="#B18-signals-05-00039" class="html-bibr">18</a>]. The grid’s origin <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> is positioned in the upper-left corner, with point <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> marking the line’s starting point at the top left, and point <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>11</mn> <mo>,</mo> <mn>5</mn> <mo>)</mo> </mrow> </semantics></math> indicating the line’s endpoint at the lower right.</p>
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<p>Example text “Lorem ipsum dolor sit amet” is warped following the <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </semantics></math> polynomial function.</p>
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<p>The padded image, with a red outline indicating the estimated curve, along with a subtle zebra pattern to emphasize the dimensions of the newly padded area.</p>
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<p>Display of all the line segments across the estimated curve, delineating the region of interest.</p>
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<p>The sample points on the curve are represented by red dots, while the control points are indicated by green dots. The lines connecting these control points are shown in blue.</p>
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<p>The semi-processed image, prior to the final alignment step.</p>
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<p>The final image, fully processed and nearly perfectly aligned, ensuring it is easily readable by both humans and computers.</p>
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<p>A schematic diagram illustrating the data processing workflow in the proposed method.</p>
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<p>(<b>Top</b>): Image displaying slanted text prior to rectification. (<b>Bottom</b>): The same text after undergoing simple vertical adjustments.</p>
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<p>(<b>Top</b>): Image displaying arched text prior to rectification. (<b>Bottom</b>): The same text after undergoing simple vertical adjustments.</p>
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15 pages, 2242 KiB  
Article
Detection of Movement and Lead-Popping Artifacts in Polysomnography EEG Data
by Nishanth Anandanadarajah, Amlan Talukder, Deryck Yeung, Yuanyuan Li, David M. Umbach, Zheng Fan and Leping Li
Signals 2024, 5(4), 690-704; https://doi.org/10.3390/signals5040038 - 22 Oct 2024
Viewed by 1001
Abstract
Polysomnography (PSG) measures brain activity during sleep via electroencephalography (EEG) using six leads. Artifacts caused by movement or loose leads distort EEG measurements. We developed a method to automatically identify such artifacts in a PSG EEG trace. After preprocessing, we extracted power levels [...] Read more.
Polysomnography (PSG) measures brain activity during sleep via electroencephalography (EEG) using six leads. Artifacts caused by movement or loose leads distort EEG measurements. We developed a method to automatically identify such artifacts in a PSG EEG trace. After preprocessing, we extracted power levels at frequencies of 0.5–32.5 Hz with multitaper spectral analysis using 4 s windows with 3 s overlap. For each resulting 1 s segment, we computed segment-specific correlations between power levels for all pairs of leads. We then averaged all pairwise correlation coefficients involving each lead, creating a time series of segment-specific average correlations for each lead. Our algorithm scans each averaged time series separately for “bad” segments using a local moving window. In a second pass, any segment whose averaged correlation is less than a global threshold among all remaining good segments is declared an outlier. We mark all segments between two outlier segments fewer than 300 s apart as artifact regions. This process is repeated, removing a channel with excessive outliers in each iteration. We compared artifact regions discovered by our algorithm to expert-assessed ground truth, achieving sensitivity and specificity of 80% and 91%, respectively. Our algorithm is an open-source tool, either as a Python package or a Docker. Full article
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<p>Overall workflow of the proposed method. For raw EEG data, the algorithm first performs the preprocessing step. Next, the algorithm computes pairwise correlation coefficients in EEG power between every pair of channels. For each channel, the correlations with the other channels are averaged. Based on the correlation coefficients, the algorithm iteratively identifies channels with excessive outliers and recomputes the average correlation. Finally, outlier segments are identified and annotated.</p>
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<p>An illustration of an electrode lead popped during recording. The left panel shows the three pairwise correlations among channels C3, F3, and F4 plotted against sleep time for a single subject. Each blue dot represents the Spearman correlation coefficient between the EEG power levels in two channels in one segment. The right panel shows the overnight spectrograms for the three channels. Colors from cool to warm indicate low to high power, respectively.</p>
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<p>An illustration of the effect of sequentially eliminating channels found to have an excessive number of outlier segments on the average correlation time series for a given channel. Each panel represents a time series of average correlations for channel F4. Top panel: average calculated from all five pairwise correlations that include channel F4. Middle panel: average calculated from four of five pairwise correlations (omitting the F4–C4 correlation). Bottom panel: average calculated from three of five pairwise correlations (omitting F4–C4 and F4–F3 correlations). Each blue dot represents the average of pairwise Spearman correlation coefficients appropriate to the particular panel.</p>
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<p>An illustration comparing expert-annotated artifact regions and algorithm-identified artifact regions in channel C3 for a single subject. Top panel: timing of NREM and REM sleep cycles. Second panel from top: spectrogram with frequency (Hz) on the Y axis, time on the X axis, and EEG power color-coded with cool to warm representing low to high power. Third panel from top: algorithm-identified artifact regions marked as black bands. Bottom panel: expert-annotated artifact regions marked as black bands.</p>
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<p>Time-series plots of correlation coefficients for all 15 possible pairs of the six channels for one subject. Each blue dot represents the Spearman correlation coefficient between the EEG power levels in two channels at one 1 s time segment. Bars at the top of each column indicate the sleep stage (NREM or REM).</p>
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<p>Spectrograms for each of the six channels for one subject, together with graphical depictions of sleep stage (NREM vs. REM or, more finely, Wake, REM, N1, N2, and N3).</p>
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<p>Artifact regions as annotated by the algorithm for each of the six channels. Black vertical bars mark artifact regions.</p>
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31 pages, 1004 KiB  
Article
Daily Streamflow Forecasting Using AutoML and Remote-Sensing-Estimated Rainfall Datasets in the Amazon Biomes
by Matteo Bodini
Signals 2024, 5(4), 659-689; https://doi.org/10.3390/signals5040037 - 10 Oct 2024
Viewed by 1194
Abstract
Reliable streamflow forecasting is crucial for several tasks related to water-resource management, including planning reservoir operations, power generation via Hydroelectric Power Plants (HPPs), and flood mitigation, thus resulting in relevant social implications. The present study is focused on the application of Automated Machine-Learning [...] Read more.
Reliable streamflow forecasting is crucial for several tasks related to water-resource management, including planning reservoir operations, power generation via Hydroelectric Power Plants (HPPs), and flood mitigation, thus resulting in relevant social implications. The present study is focused on the application of Automated Machine-Learning (AutoML) models to forecast daily streamflow in the area of the upper Teles Pires River basin, located in the region of the Amazon biomes. The latter area is characterized by extensive water-resource utilization, mostly for power generation through HPPs, and it has a limited hydrological data-monitoring network. Five different AutoML models were employed to forecast the streamflow daily, i.e., auto-sklearn, Tree-based Pipeline Optimization Tool (TPOT), H2O AutoML, AutoKeras, and MLBox. The AutoML input features were set as the time-lagged streamflow and average rainfall data sourced from four rain gauge stations and one streamflow gauge station. To overcome the lack of training data, in addition to the previous features, products estimated via remote sensing were leveraged as training data, including PERSIANN, PERSIANN-CCS, PERSIANN-CDR, and PDIR-Now. The selected AutoML models proved their effectiveness in forecasting the streamflow in the considered basin. In particular, the reliability of streamflow predictions was high both in the case when training data came from rain and streamflow gauge stations and when training data were collected by the four previously mentioned estimated remote-sensing products. Moreover, the selected AutoML models showed promising results in forecasting the streamflow up to a three-day horizon, relying on the two available kinds of input features. As a final result, the present research underscores the potential of employing AutoML models for reliable streamflow forecasting, which can significantly advance water-resource planning and management within the studied geographical area. Full article
(This article belongs to the Special Issue Rainfall Estimation Using Signals)
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Figure 1

Figure 1
<p>Map representation of the upper Teles Pires River basin. On the left side, a map of the state of Brazil delineates the boundaries of all its 27 federal states. In particular, the Teles Pires River basin extends across the states of Mato Grosso and Pará. On the right side, both the entire basin and the upper basin of the Teles Pires River are represented, where the latter one is reported with latitude and longitude coordinates. The figure reported by Oliveira et al. [<a href="#B30-signals-05-00037" class="html-bibr">30</a>] under the terms of the Creative Commons Attribution License—CC BY 4.0 (<a href="https://creativecommons.org/licenses/by/4.0/" target="_blank">https://creativecommons.org/licenses/by/4.0/</a> accessed on 1 September 2024).</p>
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<p>Characterization map of the upper Teles Pires River basin reporting a digital elevation model. The reported altitudes range from a minimum altitude of 272 m to a maximum of 895 m and are color-coded according to the reported legend on the left side. The entire drainage network, fluviometric, pluviometric, and meteorological stations are reported on the map. Figure adapted from Oliveira et al. [<a href="#B30-signals-05-00037" class="html-bibr">30</a>] under the terms of the Creative Commons Attribution License—CC BY 4.0 (<a href="https://creativecommons.org/licenses/by/4.0/" target="_blank">https://creativecommons.org/licenses/by/4.0/</a> accessed on 1 September 2024).</p>
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<p>The Figure reports the average streamflow <math display="inline"><semantics> <msub> <mover> <mi>Q</mi> <mo>¯</mo> </mover> <mi>d</mi> </msub> </semantics></math> (in m<sup>3</sup> s<sup>−1</sup>) recorded at the Teles Pires Fluviometric Station identified with code 017210000 (Latitude: −12.67º and Longitude: −55.79º) in <a href="#signals-05-00037-t001" class="html-table">Table 1</a> over the period from January 1985 to November 2023. The data shows significant seasonal fluctuations over months. Indeed, as reported in <a href="#sec3dot1-signals-05-00037" class="html-sec">Section 3.1</a>, peak rainfall usually occurs from October to April (rainy season), resulting in higher streamflow during such months, while the lowest precipitation period is from May to September (dry season), thus leading to lower induced streamflow (refer to <a href="#sec1-signals-05-00037" class="html-sec">Section 1</a> to deepen the relationship between rainfall and river flows).</p>
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<p>The top four subplots in the Figure report the rainfall data collected from the four rain gauge stations listed in <a href="#signals-05-00037-t001" class="html-table">Table 1</a>. Each subplot shows the total rainfall over time for the respective station on the <span class="html-italic">y</span>-axis. The final subplot displays the computed average daily rainfall, <math display="inline"><semantics> <msub> <mover> <mi>P</mi> <mo>¯</mo> </mover> <mi>d</mi> </msub> </semantics></math>, in red, calculated using the Thiessen polygon method. The data spans from January 1985 to November 2023, with the <span class="html-italic">x</span>-axis representing the measurement years for all the subplots. Additional details from <a href="#signals-05-00037-t001" class="html-table">Table 1</a>, such as station names, types, and geographical coordinates, were also reported.</p>
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<p>The four subplots in the Figure report the average rainfall data <math display="inline"><semantics> <msub> <mover> <mi>P</mi> <mo>¯</mo> </mover> <mi>d</mi> </msub> </semantics></math> computed from the four remote-sensing products, listed in <a href="#signals-05-00037-t002" class="html-table">Table 2</a>. Each subplot shows the average rainfall over time for the respective remote-sensing product on the <span class="html-italic">y</span>-axis. The time-spans for the computed averages are reported in the title of each subplot, with the <span class="html-italic">x</span>-axis representing the measurement years.</p>
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<p>The figure reports the forecasting performance gained by AutoML models for each selected metric, over all the employed features. The figure reports the test set forecasting performance through five separate subplots, each corresponding to a different performance metric, previously described in <a href="#sec3dot4-signals-05-00037" class="html-sec">Section 3.4</a>. Results are displayed by providing summary statistics in each subplot through box plots, color-coded with different colors, each representing a different time-lag (refer to the legends).</p>
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<p>The figure reports the forecasting performance gained for each metric when each selected feature was used as input over all the employed AutoML models. The figure reports the test set forecasting performance through five separate subplots, each corresponding to a different performance metric, previously described in <a href="#sec3dot4-signals-05-00037" class="html-sec">Section 3.4</a>. Results are displayed by providing summary statistics in each subplot through box plots, color-coded with different colors, each representing a different time-lag (refer to the legends).</p>
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<p>Average streamflow observed data and predictions obtained from the top performing AutoML model for each input feature. In the figure, AutoML models were evaluated on the data contained in the respective test set kept for each feature set (refer to <a href="#signals-05-00037-t003" class="html-table">Table 3</a>) and for each selected time-lag <span class="html-italic">l</span> (<math display="inline"><semantics> <mrow> <mn>1</mn> <mo>≤</mo> <mi>l</mi> <mo>≤</mo> <mn>3</mn> </mrow> </semantics></math>). The latter data were unseen by the trained AutoML models for all the selected input features. The reported top performing AutoML models and respective input features according to the <math display="inline"><semantics> <msubsup> <mi>AutoML</mi> <mi>score</mi> <mi mathvariant="normal">T</mi> </msubsup> </semantics></math> metric were H2O AutoML for Thiessen, auto-sklearn for PERSIANN, H2O AutoML for PERSIANN-CCS, AutoKeras for PERSIANN-CDR, and auto-sklearn for PDIR-Now. Observed average streamflow data were reported in red color, while time-series data predicted from AutoML models were reported with blue dashed lines. Horizontal thick black lines define the boundaries outside which predictions were not computed (since data were contained in the training set or were not available for the considered feature set).</p>
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17 pages, 1252 KiB  
Article
Interpretability of Methods for Switch Point Detection in Electronic Dance Music
by Mickaël Zehren, Marco Alunno and Paolo Bientinesi
Signals 2024, 5(4), 642-658; https://doi.org/10.3390/signals5040036 - 8 Oct 2024
Viewed by 1043
Abstract
Switch points are a specific kind of cue point that DJs carefully look for when mixing music tracks. As the name says, a switch point is the point in time where the current track in a DJ mix is replaced by the upcoming [...] Read more.
Switch points are a specific kind of cue point that DJs carefully look for when mixing music tracks. As the name says, a switch point is the point in time where the current track in a DJ mix is replaced by the upcoming track. Being able to identify these positions is a first step toward the interpretation and the emulation of DJ mixes. With the aim of automatically detecting switch points, we evaluate one experience-driven and several statistics-driven methods. By comparing the decision process of each method, contrasted by their performance, we deduce the characteristics linked to switch points. Specifically, we identify the most impactful features for their detection, namely, the novelty in the signal energy, the timbre, the number of drum onsets, and the harmony. Furthermore, we expose multiple interactions among these features. Full article
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Figure 1
<p>Algorithmic workflow for both the data- and the experience-driven methods introduced in this article.</p>
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<p>Visual example of the search space identified.</p>
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<p>Quantitative evaluation: Mean precision and mean recall on the EDM-150 dataset. The reported values are the average of the five test splits and the error bars represent the standard deviation. For the experience-driven model, instead, the evaluation is performed only once on the whole dataset.</p>
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<p>Coefficients learned by LC-LDA.</p>
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<p>Decision tree trained on the whole EDM-150. The root node represents the initial distribution of the ground truth labels. Traversing down the tree, the candidates are divided according to the learned decision rules toward the child nodes until reaching the leaves of the tree.</p>
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<p>SHAP summary plot from the Boosting trees model.</p>
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<p>SHAP dependence and interaction plots for energy novelty: (<b>a</b>) SHAP dependence plot: log relative probability to detect a switch point depending on energy novelty. The spread of the values is mainly due to interaction with timbre novelty. (<b>b</b>) Main effect of energy novelty, without the interaction effect of the other features. The interaction effects of energy novelty with bass drum novelty or timbre novelty are represented in (<b>c</b>) and (<b>d</b>), respectively.</p>
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9 pages, 2212 KiB  
Article
Adaptive Filtering for Multi-Track Audio Based on Time–Frequency Masking Detection
by Wenhan Zhao and Fernando Pérez-Cota
Signals 2024, 5(4), 633-641; https://doi.org/10.3390/signals5040035 - 2 Oct 2024
Viewed by 858
Abstract
There is a growing need to facilitate the production of recorded music as independent musicians are now key in preserving the broader cultural roles of music. A critical component of the production of music is multitrack mixing, a time-consuming task aimed at, among [...] Read more.
There is a growing need to facilitate the production of recorded music as independent musicians are now key in preserving the broader cultural roles of music. A critical component of the production of music is multitrack mixing, a time-consuming task aimed at, among other things, reducing spectral masking and enhancing clarity. Traditionally, this is achieved by skilled mixing engineers relying on their judgment. In this work, we present an adaptive filtering method based on a novel masking detection scheme capable of identifying masking contributions, including temporal interchangeability between the masker and maskee. This information is then systematically used to design and apply filters. We implement our methods on multitrack music to improve the quality of the raw mix. Full article
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Figure 1
<p>Calculation of masking in the temporal and spectral dimensions using short-time Fourier transforms. The time–frequency spectrum of tracks 1 ((<b>a</b>), bass) and 2 ((<b>b</b>), guitar) was obtained using short-time Fourier transforms. (<b>c</b>) Masking between track 1 and track 2 as given by Equation (<a href="#FD2-signals-05-00035" class="html-disp-formula">2</a>). The positive values in (<b>c</b>) indicate the masking of track 1 over track 2 while the negative values in (<b>c</b>) indicate the masking of track 2 over track 1.</p>
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<p>Calculation of masking in the frequency domain. (<b>a</b>) The masking matrix <math display="inline"><semantics> <mrow> <msubsup> <mi>M</mi> <mn>12</mn> <mo>′</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> is compressed to a single dimension (<math display="inline"><semantics> <mrow> <msubsup> <mi>M</mi> <mn>12</mn> <mo>′</mo> </msubsup> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>) using Equation (<a href="#FD3-signals-05-00035" class="html-disp-formula">3</a>). (<b>b</b>,<b>c</b>) Masking of track 1 over track 2 (<math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>,red) and track 2 over track 1 (<math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>,blue) are separated using Equations (<a href="#FD4-signals-05-00035" class="html-disp-formula">4</a>) and (<a href="#FD5-signals-05-00035" class="html-disp-formula">5</a>), respectively. (<b>d</b>) The final masking of T<sub>r1</sub>, T<sub>r2</sub>…T<sub>rN</sub> over others (<math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mrow> <mi>T</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mrow> <mi>T</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> … <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mrow> <mi>T</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>), which is used for filter design (green), was calculated using Equation (<a href="#FD6-signals-05-00035" class="html-disp-formula">6</a>). In this equation, the contributions to masking from each track over the others (i.e., M<sub>1,2</sub>,M<sub>1,3</sub>…M<sub>1,N</sub>) are averaged and normalised. The same process can be expanded to any number of tracks (see the Results section).</p>
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<p>Filter design. (<b>a</b>) Masking matrix (orange) with peaks identified (blue stars). (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mrow> <mi>T</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> with adaptive threshold (blue) and noise floor (dashed green). (<b>c</b>) Only the peaks above the adaptive threshold remain and are used for filter design. (<b>d</b>) Frequency response of the final filter for track 1 with a user-defined gain of 3 dB (yellow) and showing the peaks (orange stars) used for the design.</p>
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<p>Masking detected for S<sub>1</sub>. The positive masking (red) represents a track 1 masking track 2 while negative masking (yellow) represents track2 masking track1. (<b>a</b>) Bass (1) over accordion (2). (<b>b</b>) Bass (1) over vocals (2). (<b>c</b>) Bass (1) over guitar (2). (<b>d</b>) Accordion (1) over guitar (t2). (<b>e</b>) Accordion (1) over vocals (2). (<b>f</b>) Vocals (1) over guitar (2).</p>
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<p>Filters generated and applied to each track. Each track had its own filter applied, which was generated through the analysis of the relationships between the tracks. The filters attenuate each track at different bands, except for guitar and vocals which share an attenuation peak at 165 Hz.</p>
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<p>Relationships between source tracks and final masking vectors for the four tracks of the multitrack from <span class="html-italic">Flesh and Bone</span>. The same process can be expanded for any number of tracks.</p>
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<p>Multitrack spectrum and excerpt before and after filtering. (<b>a</b>,<b>b</b>) bass, (<b>c</b>,<b>d</b>) accordion, (<b>e</b>,<b>f</b>) vocals, and (<b>g</b>,<b>h</b>) guitar. Bass and accordion show the most prominent differences as gains for the filters were more aggressive. The spectral differences match those seen in <a href="#signals-05-00035-f005" class="html-fig">Figure 5</a>.</p>
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