CN105006233A - Narrowband feedforward active noise control system and target noise suppression method - Google Patents

Abstract

The present invention discloses a narrowband feedforward active noise control system and a target noise suppression method which belong to the narrowband active noise control technology field. The system comprises a frequency tracking and reference signal generating module, a reference signal delay module, a first amplitude phase regulating module, a second amplitude phase regulating module, a first accumulation module, a secondary channel, a second accumulation module, a first parameter regulating module, a second parameter regulating module and a third parameter regulating module. A reference signal of the method is generated by an AR model according to the source noise frequency picked up by a non-acoustic sensor, a part of secondary source is generated by an amplitude phase regulator, and the other part of secondary source is generated by a delay module and the other one amplitude phase regulator. When the non-acoustic sensor exists an error, the two parts of secondary source is synthesized to be superposed with the target noise, so that more than 10% of frequency mismatching amount can be replied effectively, and the system is fast in convergence speed.

Description

Narrow-band feedforward active noise control system and target noise suppression method

Technical Field

The invention discloses a narrow-band feedforward Active Noise Control system and a target Noise suppression method, and belongs to the technical field of narrow-band Active Noise Control (ANC).

Background

Compared with a passive noise control method, the active noise control method has the advantages of good low-frequency characteristic, small controller size and the like, and is very suitable for suppressing periodic or approximately periodic low-frequency sinusoidal narrow-band noise. Such narrow-band noise is often generated by rotating equipment or devices having reciprocating motion. In narrow-band active noise control, in order to avoid acoustic feedback, the noise frequency is often measured directly or indirectly by a non-acoustic sensor, and according to the measured synchronous frequency, a sinusoidal reference signal with the same frequency is generated by a signal generator and provided to a control filter to generate secondary noise for canceling target noise.

Due to long-time operation, aging and the like of the non-acoustic sensor, an error exists between the measured synchronous frequency and the true frequency of the target noise, namely, a frequency mismatching phenomenon is generated. At this time, the narrow-band active noise control system is difficult to effectively deal with, and the noise suppression effect is seriously reduced.

Disclosure of Invention

The technical problem to be solved by the present invention is to provide a narrowband feedforward active noise control system and a target noise suppression method for overcoming the above-mentioned shortcomings of the background art, so that the narrowband active noise control system can track the target noise frequency when there is frequency mismatch, and the technical problems of large calculation amount and low convergence speed when the narrowband feedforward ANC system deals with the frequency mismatch are solved.

The invention adopts the following technical scheme for realizing the aim of the invention:

a narrow-band feedforward active noise control system comprising: a frequency tracking and reference signal generating module, a reference signal delay module, a first amplitude phase adjusting module, a second amplitude phase adjusting module, a first accumulating module, a secondary channel, a second accumulating module, a first parameter adjusting module, a second parameter adjusting module, and a third parameter adjusting module,

the frequency tracking and reference signal generation module: the output end of the reference signal delay module is connected with the input end of the reference signal delay module and the input end of the first amplitude phase adjusting module, the frequency of the target noise is tracked under the synchronous frequency acquired by the non-acoustic sensor by adopting an AR model, a sinusoidal reference signal is generated, and the sinusoidal reference signal is output to the reference signal delay module and the first amplitude phase adjusting module;

a reference signal delay module: the output end of the delay reference signal is connected with the input end of the second amplitude phase module, and the delay reference signal is output to the second amplitude phase adjusting module;

a first accumulation module: one input end is connected with the output end of the first amplitude phase adjusting module, the other input end is connected with the output end of the second amplitude phase adjusting module, the output end is connected with the input end of the secondary channel, and the secondary source composite signal is output to the secondary channel after receiving a part of secondary source signals output by the first amplitude phase adjusting module and the other part of secondary source signals output by the second amplitude phase adjusting module;

a second accumulation module: one input end is connected with the output end of the secondary channel, the other input end is connected with the target noise signal, and the residual noise signal is output after the target noise signal and the secondary noise signal output by the secondary channel are received;

a first parameter adjustment module: one input end is connected with a filtering signal of the sine type reference signal, the other input end is connected with a residual noise signal, and a parameter updating value of the first amplitude phase adjusting module is output;

a second parameter adjustment module: one input end is connected with the filtering signal of the delay reference signal, the other input end is connected with the residual noise signal, and the parameter updating value of the second amplitude phase adjusting module is output;

a third parameter adjustment module: one input end is connected with a filtering signal of a sine type reference signal, the other input end is connected with a residual noise signal, and an adaptive parameter updating value of a frequency tracking and reference signal generating module is output.

Further, in the narrowband active noise control system, the first amplitude phase adjustment module is a first FIR filter, and the second amplitude phase adjustment module is a second FIR filter.

Still further, in the narrowband active noise control system, the first parameter adjusting module, the second parameter adjusting module, and the third parameter adjusting module all use an LMS algorithm to update parameters.

Further, in the narrow-band active noise control system, the target noise signal is generated by the superposition of the narrow-band noise generated at the cancellation point by the narrow-band noise source propagating through the linear primary channel and the environmental random noise.

The target noise suppression method is realized by adopting the system and comprises the following steps:

A. acquiring a reference signal: the frequency tracking and reference signal generating module generates a sinusoidal reference signal under the synchronous frequency acquired by the non-acoustic sensor, and the reference signal delay module processes the sinusoidal reference signal to obtain a delayed reference signal;

B. acquisition of the secondary source synthesis signal: the first FIR filter performs amplitude phase adjustment on the sinusoidal reference signal to obtain a part of secondary source signals, the second FIR filter performs amplitude phase adjustment on the delayed reference signal to obtain another part of secondary source signals, and the part of secondary source signals and the other part of secondary source signals are superposed by a first accumulator to obtain secondary source synthesized signals;

C. suppression of target noise signal: the secondary source synthetic signal generates a secondary noise signal through a secondary channel, and the secondary noise signal and the target noise signal are subjected to superposition cancellation through a second adder to obtain a residual noise signal;

D. updating parameters: the method comprises the steps that a secondary channel estimation model is adopted to process a sinusoidal reference signal and a delay reference signal to obtain a filtering-X reference signal and a filtering-X delay reference signal, a first parameter adjusting module updates the weight of a first FIR filter according to the filtering-X reference signal and a residual noise signal, a second parameter adjusting module updates the weight of a second FIR filter according to the filtering-X delay reference signal and the residual noise signal, and a third parameter adjusting module updates the self-adaptive parameters of a frequency tracking and reference signal generating module according to the filtering-X reference signal and the residual noise signal.

Further, in the target noise suppression method, the sinusoidal reference signal generated in step a is:

x_i(n)＝-c_i(n)x_i(n-1)-x_i(n-2),n≥2

x_i(0)＝a_i

x_i(1)＝a_i cos(ω_i(0))+b_i sin(ω_i(0) in a batch process), wherein,

x_i(0)、x_i(1)、x_i(n-2)、x_i(n-1)、x_i(n) the updating values of the 0 th time, the 1 st time, the n-2 th time, the n-1 st time and the n-th time of the sinusoidal reference signal respectively, c_i(n) is the nth update value of the adaptive parameter, ω_i(0) For synchronous frequencies measured by non-acoustic sensors, adaptive parameter initialization values c_i(0)：c_i(0)＝-2cos(ω_i(0))。

Still further, in the target noise suppression method, a part of the secondary source signal obtained in step B is usedAnd another part of the secondary source signalRespectively as follows:

$\begin{array}{c}{y}_i^{\left(0\right)}\left(n\right)=h_{i,0}^{\left(0\right)}\left(n\right)x_i\left(n\right)+h_{i,1}^{\left(0\right)}\left(n\right)x_i(n-1)\\ y_i^{(-k)}\left(n\right)=h_{i,0}^{(-k)}\left(n\right)x_i(n-k)+h_{i,1}^{(-k)}\left(n\right)x_i(n-k-1)\end{array},$ wherein,

is the nth updated value, x, of the first FIR filter weight_i(n-1)、x_i(n) is the n-1 th and n-th updated values of the sine type reference signal,is the nth updated value, x, of the second FIR filter weight_i(n-k-1)、x_i(n-k) is the n-1 th and n-th updated values of the delayed reference signal.

Further, in the target noise suppression method, the target noise p (n) in step C is:

<math> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>q</mi> </munderover> <mo>[</mo> <msub> <mi>a</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>x</mi> <msub> <mi>a</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>x</mi> <msub> <mi>b</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <msub> <mi>v</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> wherein,

q is the number of frequency components in the target noise, a_p,i、b_p,iIn order to be a discrete fourier coefficient,in the form of a cosine signal component,for the components of the sinusoidal signal to be, <math> <mrow> <msub> <mi>x</mi> <msub> <mi>a</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>x</mi> <msub> <mi>b</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> ω_p,ifor the target noise signal frequency, v_pAnd (n) is ambient random noise.

As a further optimization scheme of the target noise suppression method, an update equation of the first FIR filter weight in step D is: <math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> the update equation of the second FIR filter weight is: <math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> the update equation of the adaptive parameters of the frequency tracking and reference signal generation module is as follows: <math> <mrow> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&mu;</mi> <msub> <mi>c</mi> <mi>i</mi> </msub> </msub> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> wherein,

the n +1 th updated value of the first FIR filter weight, the n +1 th updated value of the second FIR filter weight,for the n-1 th and nth update values of the filtered-X reference signal,delaying the n-1 th, n-th update value, mu, of the reference signal for filtering-X_iThe update coefficients for the sinusoidal reference signal and the delayed reference signal,the coefficients are updated for the adaptive parameters.

By adopting the technical scheme, the invention has the following beneficial effects:

(1) the frequency tracking and reference signal generating module utilizes the self-adaptive notch filter to track the frequency of a noise target, can effectively track the frequency of the target noise and generate a sinusoidal reference signal related to the target noise;

(2) the added reference signal delay module and part of secondary sources generated by the second amplitude phase module and part of secondary sources obtained by amplitude phase adjustment of the reference signal are subjected to superposition cancellation to generate residual noise with minimum energy, and the convergence speed of the system is improved with less calculation amount;

(3) the introduction of the reference delay signal module and the amplitude phase adjusting module influences the parameter updating of the AR model frequency tracking and reference signal generating module, so that the frequency mismatching amount of the whole system can reach more than 10%, and the method is easy to realize in an actual active noise controller;

(4) the target noise suppression method is easy to realize frequency mismatching response under multiple frequency channels through simple parallel extension, and achieves the purpose of effectively suppressing narrow-band noise.

Drawings

Fig. 1 is a schematic block diagram of a narrowband active noise control system of the present invention.

The reference numbers in the figures illustrate: 1. the device comprises a frequency tracking and reference signal generating module, 2, a reference signal delay module, 31, a first amplitude phase adjusting module, 32, a second amplitude phase adjusting module, 41, a first parameter adjusting module, 42, a second parameter adjusting module, 43, a third parameter adjusting module, 5, a first accumulation module, 6, a secondary channel, 7 and a second accumulation module.

Detailed Description

The technical scheme of the invention is explained in detail in the following with reference to the attached drawings.

The invention provides a method for dealing with frequency mismatching in narrow-band active noise control, which is further described in detail by referring to the attached drawings and taking examples in order to make the purpose, technical scheme and effect of the invention clearer and clearer. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

The principle of the narrow-band active noise control system provided by the invention is shown in fig. 1, and the narrow-band active noise control system comprises: the system comprises a frequency tracking and reference signal generating module 1, a reference signal delaying module 2, two amplitude phase adjusting modules (namely a first amplitude phase adjusting module 31 and a second amplitude phase adjusting module 32), three least mean square algorithm modules (namely a first parameter adjusting module 41, a second parameter adjusting module 42 and a third parameter adjusting module 43), a first accumulating module 5, a secondary channel 6 and a second accumulating module 7. The output end of the frequency tracking and reference signal generating module 1 is connected with the input end of the reference signal delay module 2 and the input end of the first amplitude phase adjusting module 31, the output end of the reference signal delay module 2 is connected with the input end of the second amplitude phase module 32, one input end of the first accumulating module 5 is connected with the output end of the first amplitude phase adjusting module 31, the other input end of the first accumulating module 5 is connected with the output end of the second amplitude phase adjusting module 32, the output end of the first accumulating module 5 is connected with the input end of the secondary channel 6, one input end of the second accumulating module 7 is connected with the output end of the secondary channel 6, the other input end of the second accumulating module 7 is connected with the target noise signal, one input end of the first parameter adjusting module 41 is connected with the filtering signal of the sinusoidal reference signal, the other input end of the first parameter adjusting module 41 is connected with the residual noise signal, one input end of the second parameter, the other input of the second parameter adjustment module 42 is connected to the residual noise signal, one input of the third parameter adjustment module 43 is connected to the filtered signal of the sinusoidal reference signal, and the other input of the third parameter adjustment module 43 is connected to the residual noise signal.

The frequency tracking and reference signal generating module 1 is composed of an AR model, and is used for automatically tracking the noise frequency and generating a reference signal at the same time under the condition of a given frequency initial value. The amplitude phase adjusting modules are all first-order FIR filters, after being superposed, part of secondary source signals generated by the first-order FIR filters are superposed with a target noise signal through a secondary channel 6 to form a cancellation suppression effect, and a reference signal delay module 2 is arranged in front of the second amplitude phase adjusting module 32 to generate a delay reference signal which is input by the second amplitude phase adjusting module 32. The adaptive parameters in the frequency tracking and reference signal generation module 1 and the filter weights of the amplitude phase adjustment module are respectively subjected to adaptive adjustment by the least mean square algorithm modules 43, 41 and 42;

the method for suppressing the target noise corresponding to the frequency mismatch comprises the following steps:

step 1, a frequency tracking and reference signal generating module 1 generates a sinusoidal reference signal according to a synchronous frequency signal obtained by a non-acoustic sensor, and provides the sinusoidal reference signal to a first amplitude phase adjusting module 31;

the reference signal passes through the delay module 2 to form a delayed reference signal, and the delayed reference signal is provided to the second amplitude phase adjustment module 32;

target noise p (n) is the noise formed at the point of cancellation after the narrow-band source noise has propagated through the linear primary channel, and can be expressed as

<math> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>q</mi> </munderover> <mo>[</mo> <msub> <mi>a</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>x</mi> <msub> <mi>a</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>x</mi> <msub> <mi>b</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <msub> <mi>v</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>

Wherein q is the number of frequency components in the target noise, a_p,i、b_p,iIn order to be a discrete fourier coefficient,in the form of a cosine signal component,for the components of the sinusoidal signal to be, <math> <mrow> <msub> <mi>x</mi> <msub> <mi>a</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>x</mi> <msub> <mi>b</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> ω_p,iis the target noise frequency, v_p(n) is additive environmental noise;

the sinusoidal reference signal generated by the frequency tracking and reference signal generating module 1 is:

x_i(n)＝-c_i(n)x_i(n-1)-x_i(n-2),n≥2

x_i(0)＝a_i

x_i(1)＝a_i cos(ω_i(0))+b_i sin(ω_i(0))

wherein x is_i(0)、x_i(1)、x_i(n-2)、x_i(n-1)、x_i(n) the updating values of the 0 th time, the 1 st time, the n-2 th time, the n-1 st time and the n-th time of the sinusoidal reference signal respectively, c_i(n) is the nth updated value of the adaptive parameter; omega_i(0) For the synchronous frequency measured by the non-acoustic sensor, when the non-acoustic sensor has an error, the frequency value is equal to the target noise frequency omega_p,iThere is a deviation therebetween. Parameter c_i(n) reflects the frequency tracking effect, and its initial value may be set to: c. C_i(0)＝c_i(1)＝-2cos(ω_i(0))。

Step 2, the first amplitude phase adjusting module 31 performs amplitude phase adjustment on the reference signal to generate a part of secondary source signals

The delayed reference signal is amplitude-phase adjusted by a second amplitude-phase adjusting module 32 to generate another part of secondary source signal

The amplitude phase adjusting modules 31 and 32 are both first-order FIR filters, and output part of secondary source signalsAndcomprises the following steps:

$y_i^{\left(0\right)}\left(n\right)=h_{i,0}^{\left(0\right)}\left(n\right)x_i\left(n\right)+h_{i,1}^{\left(0\right)}\left(n\right)x_i(n-1)$

$y_i^{(-k)}\left(n\right)=h_{i,0}^{(-k)}\left(n\right)x_i(n-k)+h_{i,1}^{(-k)}\left(n\right)x_i(n-k-1)$

is the nth updated value, x, of the first FIR filter weight_i(n-1)、x_i(n) is the n-1 th and n-th updated values of the sine type reference signal,is the nth updated value, x, of the second FIR filter weight_i(n-k-1)、x_i(n-k) is the n-1 th and nth updated values of the delayed reference signal;

the method also provides three least mean square algorithm modules 41, 42 and 43, and the secondary channel S (z) is estimated by an off-line identification method (or an on-line identification method) to obtain an estimation modelSinusoidal reference signal estimated modelProcessing to obtain a filtered-X reference signal, which is used as an input signal of the least mean square algorithm module 41 together with the residual noise e (n); delayed reference signal estimated modelThe filtered-X delayed reference signal is processed and used together with the residual noise e (n) as an input signal of the least mean square algorithm module 42; sinusoidal reference signal estimated modelThe filtered-X reference signal is processed and used together with the residual noise e (n) as the input signal of the least mean square algorithm module 43;

the least mean square algorithm module 41 is an update controller of the filter weights in the first amplitude phase adjustment module 31; the least mean square algorithm module 42 is an update controller of the filter weights in the second amplitude phase adjustment module 32; the least mean square algorithm module 43 is an update controller of adaptive parameters in the frequency tracking and reference signal generation module 1; updating the weight and the parameters by using a gradient descent method, and enabling the residual noise energy obtained after the synthesized secondary noise is cancelled with the target noise to be minimum by adjusting the weight and the parameters of the updating filter;

updating filter weights and AR model adaptive parameters by filtering-X least mean square (FXLMS) algorithm, includingAnd c_i(n) generating secondary noise y_s(n) is effective in suppressing target noise p (n);

the filter weights of the amplitude and phase adjustment modules 31 and 32 and the adaptive parameters of the AR model of the frequency tracking and reference signal generation module 1 in the figure are updated according to the following equations:

<math> <mrow> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&mu;</mi> <msub> <mi>c</mi> <mi>i</mi> </msub> </msub> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,the n +1 th updated value of the first FIR filter weight,the n +1 th updated value of the second FIR filter weight,for the n-1 th and nth update values of the filtered-X reference signal,delaying the nth of the reference signal for filtering-X1, n-th update of value, mu_iThe update coefficients for the sinusoidal reference signal and the delayed reference signal,updating coefficients for the adaptive parameters;

true secondary channel S (z) and its estimationIt is usually composed of FIR filters, namely:

<math> <mrow> <mi>S</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>s</mi> <mi>j</mi> </msub> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mi>j</mi> </mrow> </msup> </mrow> </math>

<math> <mrow> <mover> <mi>S</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mover> <mi>M</mi> <mo>^</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mover> <mi>s</mi> <mo>^</mo> </mover> <mi>m</mi> </msub> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mi>m</mi> </mrow> </msup> </mrow> </math>

estimation via secondary channelThe filtered-X reference signal is:

<math> <mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mover> <mi>M</mi> <mo>^</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mover> <mi>s</mi> <mo>^</mo> </mover> <mi>m</mi> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>m</mi> <mo>)</mo> </mrow> </mrow> </math>

M、is the filter length.

Step 3, the secondary sourceAnd secondary sourceSuperposed and then passes through a secondary channel S (z) to output a secondary noise signal y_s(n); secondary noise signal y_s(n) carrying out destructive superposition with the target noise signal p (n) to obtain the residual noise e (n) after the destructive superposition;

the residual noise e (n) after target noise cancellation in the figure can be calculated as:

e(n)＝p(n)-y_s(n)

<math> <mrow> <msub> <mi>y</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>p</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>q</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>s</mi> <mi>j</mi> </msub> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein, y_i(n) is composed ofAndthe superposed secondary source synthesis signals are as follows:

$y_i\left(n\right)=y_i^{\left(0\right)}\left(n\right)+y_i^{(-k)}\left(n\right).$

in summary, the invention adopting the above technical scheme has the following beneficial effects:

(1) the frequency tracking and reference signal generating module utilizes the self-adaptive notch filter to track the frequency of a noise target, can effectively track the frequency of the target noise and generate a sinusoidal reference signal related to the target noise;

(2) the added reference signal delay module and part of secondary sources generated by the second amplitude phase module and part of secondary sources obtained by amplitude phase adjustment of the reference signal are subjected to superposition cancellation to generate residual noise with minimum energy, and the convergence speed of the system is improved with less calculation amount;

(3) the introduction of the reference delay signal module and the amplitude phase adjusting module influences the parameter updating of the AR model frequency tracking and reference signal generating module, so that the frequency mismatching amount of the whole system can reach more than 10%, and the method is easy to realize in an actual active noise controller;

(4) the target noise suppression method is easy to realize frequency mismatching response under multiple frequency channels through simple parallel extension, and achieves the purpose of effectively suppressing narrow-band noise.

It should be understood that the drawings are only schematic representations of one embodiment, and the blocks or processes in the drawings are not necessarily essential to practicing the invention, and may be equivalent or modified according to the spirit and scope of the invention and all such modifications or alterations should fall within the scope of the appended claims.

Claims (9)

1. A narrow-band feedforward active noise control system, comprising: a frequency tracking and reference signal generating module (1), a reference signal delay module (2), a first amplitude phase adjusting module (31), a second amplitude phase adjusting module (32), a first accumulation module (5), a secondary channel (6), a second accumulation module (7), a first parameter adjusting module (41), a second parameter adjusting module (42) and a third parameter adjusting module (43), wherein,

frequency tracking and reference signal generation module (1): the output end of the reference signal delay module (2) is connected with the input end of the reference signal delay module (2) and the input end of the first amplitude phase adjusting module (31), an AR model is adopted to track the frequency of the target noise under the synchronous frequency acquired by the non-acoustic sensor and generate a sine-shaped reference signal, and the sine-shaped reference signal is output to the reference signal delay module (2) and the first amplitude phase adjusting module (31);

reference signal delay module (2): the output end of the delay reference signal is connected with the input end of the second amplitude phase module (32), and the delay reference signal is output to the second amplitude phase adjusting module (32);

a first accumulation module (5): one input end is connected with the output end of the first amplitude phase adjusting module (31), the other input end is connected with the output end of the second amplitude phase adjusting module (32), the output end is connected with the input end of the secondary channel (6), and after receiving a part of secondary source signals output by the first amplitude phase adjusting module (31) and the other part of secondary source signals output by the second amplitude phase adjusting module (32), secondary source synthetic signals are output to the secondary channel (6);

a second accumulation module (7): one input end is connected with the output end of the secondary channel (6), the other input end is connected with the target noise signal, and the residual noise signal is output after the target noise signal and the secondary noise signal output by the secondary channel are received;

first parameter adjustment module (41): one input end is connected with a filtering signal of the sine type reference signal, the other input end is connected with a residual noise signal, and a parameter updating value of a first amplitude phase adjusting module (31) is output;

second parameter adjustment module (42): one input end is connected with the filtering signal of the delay reference signal, the other input end is connected with the residual noise signal, and the parameter updating value of the second amplitude phase adjusting module (32) is output;

third parameter adjustment module (43): one input end is connected with a filtering signal of a sine type reference signal, the other input end is connected with a residual noise signal, and an adaptive parameter updating value of the frequency tracking and reference signal generating module (1) is output.

2. The narrowband active noise control system of claim 1, wherein the first magnitude-phase adjustment module (31) is a first FIR filter and the second magnitude-phase adjustment module (32) is a second FIR filter.

3. The narrowband active noise control system according to claim 2, wherein the first parameter adjustment module (41), the second parameter adjustment module (42), and the third parameter adjustment module (43) all update parameters using an LMS algorithm.

4. The narrowband active noise control system of any of claims 1 to 3, wherein the target noise signal is generated by a superposition of narrowband noise generated at a cancellation point by a narrowband noise source propagating through the linear primary channel and ambient random noise.

5. A method for suppressing target noise, implemented by the system of claim 3, comprising the steps of:

A. acquiring a reference signal: the frequency tracking and reference signal generating module generates a sinusoidal reference signal under the synchronous frequency acquired by the non-acoustic sensor, and the reference signal delay module processes the sinusoidal reference signal to obtain a delayed reference signal;

B. acquisition of the secondary source synthesis signal: the first FIR filter performs amplitude phase adjustment on the sinusoidal reference signal to obtain a part of secondary source signals, the second FIR filter performs amplitude phase adjustment on the delayed reference signal to obtain another part of secondary source signals, and the part of secondary source signals and the other part of secondary source signals are superposed by a first accumulator to obtain secondary source synthesized signals;

C. suppression of target noise signal: the secondary source synthetic signal generates a secondary noise signal through a secondary channel, and the secondary noise signal and the target noise signal are subjected to superposition cancellation through a second adder to obtain a residual noise signal;

D. updating parameters: the method comprises the steps that a secondary channel estimation model is adopted to process a sinusoidal reference signal and a delay reference signal to obtain a filtering-X reference signal and a filtering-X delay reference signal, a first parameter adjusting module updates the weight of a first FIR filter according to the filtering-X reference signal and a residual noise signal, a second parameter adjusting module updates the weight of a second FIR filter according to the filtering-X delay reference signal and the residual noise signal, and a third parameter adjusting module updates the self-adaptive parameters of a frequency tracking and reference signal generating module according to the filtering-X reference signal and the residual noise signal.

6. The target noise suppression method of claim 5, wherein the sinusoidal reference signal generated in step A is:

x_i(n)＝-c_i(n)x_i(n-1)-x_i(n-2),n≥2

x_i(0)＝a_i

x_i(1)＝a_i cos(ω_i(0))+b_i sin(ω_i(0) in a batch process), wherein,

x_i(0)、x_i(1)、x_i(n-2)、x_i(n-1)、x_i(n) the updating values of the 0 th time, the 1 st time, the n-2 th time, the n-1 st time and the n-th time of the sinusoidal reference signal respectively, c_i(n) is the nth update value of the adaptive parameter, ω_i(0) For synchronous frequencies measured by non-acoustic sensors, adaptive parameter initialization values c_i(0)_：c_i(0)＝-2cos(ω_i(0))。

7. The method of claim 6, wherein a portion of the secondary source signal obtained in step B is used as the source signalAnd another part of the secondary source signalRespectively as follows:

$\begin{array}{c}{y}_i^{\left(0\right)}\left(n\right)=h_{i,0}^{\left(0\right)}\left(n\right)x_i\left(n\right)+h_{i,1}^{\left(0\right)}\left(n\right)x_i(n-1)\\ y_i^{(-k)}\left(n\right)=h_{i,0}^{(-k)}\left(n\right)x_i(n-k)+h_{i,1}^{(-k)}\left(n\right)x_i(n-k-1)\end{array},$ wherein,

is the nth updated value, x, of the first FIR filter weight_i(n-1)、x_i(n) is the n-1 th and n-th updated values of the sine type reference signal,is the nth updated value, x, of the second FIR filter weight_i(n-k-1)、x_i(n-k) is the n-1 th and n-th updated values of the delayed reference signal.

8. The method for suppressing target noise according to claim 7, wherein the target noise p (n) in step C is:

<math> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>q</mi> </munderover> <mo>[</mo> <msub> <mi>a</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>x</mi> <msub> <mi>a</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>x</mi> <msub> <mi>b</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <msub> <mi>v</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> wherein,

q is the number of frequency components in the target noise, a_p,i、b_p,iIn order to be a discrete fourier coefficient,in the form of a cosine signal component,for the components of the sinusoidal signal to be,ω_p,ifor the target noise signal frequency, v_pAnd (n) is ambient random noise.

9. The method of claim 8, wherein the update equation of the first FIR filter weights in step D is: <math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> the update equation of the second FIR filter weight is: <math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> the update equation of the adaptive parameters of the frequency tracking and reference signal generation module is as follows:wherein,

the n +1 th updated value of the first FIR filter weight, the n +1 th updated value of the second FIR filter weight,for the n-1 th and nth update values of the filtered-X reference signal,delaying the n-1 th, n-th update value, mu, of the reference signal for filtering-X_iThe update coefficients for the sinusoidal reference signal and the delayed reference signal,the coefficients are updated for the adaptive parameters.