CN100504400C - A High Speed Signal Reconstruction Method for Oscilloscope - Google Patents

Abstract

The invention provides a high-speed signal reconstruction method of an oscilloscope, and belongs to the technical field of high-speed broadband oscilloscopes. The method comprises the following steps: sampling an original band-limited signal x to obtain a sequence x (n), and inserting a plurality of zero-value points between two adjacent actual sampling points at equal intervals to obtain a new sequence m (n); using interpolation filters on the spectrum M (e) of M (n)^jω) Low-pass filtering to separate the baseband component X (e) of the original signal^jω) (ii) a For the baseband component X (e) of the original signal^jω) And performing inverse Fourier transform to obtain a signal after interpolation of the original signal. Wherein, the interpolation filter is constructed by adopting a frequency domain sampling method. Compared with the traditional high-speed signal reconstruction method of the oscilloscope, the method can effectively correct the waveform distortion caused by the frequency spectrum leakage, and the physical characteristics of the output signal are completely consistent with the original signal, thereby achieving the purpose of reconstructing the original signal with high quality.

Description

A kind of oscillographic high speed signal reconstruction method

Technical field

The invention belongs to high-speed wideband oscillograph technical field, be specifically related to a kind of oscillographic high speed signal reconstruction method.

Background technology

In the high-speed digital system because mismatch or do not connect reflection that the terminal transmission line causes, harass or earthyly beat, burr, concussion that bus contention produces be acyclic often; Edge signal also often includes in they important harmonic information more than the basic frequency fast.If digital oscilloscope is the bandwidth deficiency, and then the display waveform high fdrequency component reduces, and pulse edge slows down, and high frequency signal amplitude reduces, display waveform distortion even aliasing, and the hypervelocity digitized instrument that therefore is used to catch them must be with the real-time mode sampling and show.At present, utilize parallel alternative expression technology, the real-time sampling speed of hypervelocity digitizing oscilloscope has broken through 40Gsa/s; Improve real-time sampling speed but only depend on, acquisition remain signal small part sampling point, they are that disperse, abstract.For signal is investigated more intuitively and analyzed, with regard to the more details of necessary picked up signal, this requires to recover the waveform of original signal from resulting discrete sampling is worthwhile.Usually, be that means achieve the above object by the utilization signal reconstruction.

Signal reconstruction utilizes limited the resulting data value of sampling to calculate according to certain rule exactly, to determine the value of original signal on all the other each required real time points.This method is inserted a series of sample points that computing obtains through computing rule between actual samples point, can obtain the overall picture of signal and required more waveform details.

The waveform reconfiguration technique is widely used in numerous areas, as sampling rate conversion, image reconstruction, high resolving power extreme value location etc.This method also is applied in the high-speed figure storage oscilloscope, in order to recovering the waveform of input signal, and improves the measurement and the display precision of waveform under the base when very fast.For example, in digital oscilloscope, when adopting the real-time sampling mode, the waveform of seeing on the oscillograph screen is the signal waveform of being rebuild out by the sampled point in the storer.If time base shelves are too small, and sampling rate has arrived the limit, when oscillograph can't be adopted enough points and shows, just adopt interpolation algorithm between two actual samples points, to insert one or several and put and recover waveform.So digital oscilloscope is to keep the sampling number that shows on the screen enough high by calculating sampled value interpolation or that show.Interpolation algorithm show can make effective memory bandwidth near or equal the real-time sampling bandwidth, also can eliminate the vision aliasing error simultaneously.

Interpolation reconstruction is a kind of frequency inverted algorithm.With the signals sampling frequency from a given frequency $F=\frac{1}{T}$ Be transformed into the another one frequency $F\′=\frac{1}{T\′}$ Process, be called sample frequency conversion.If new sample frequency F ' is higher than original frequency F, i.e. F '〉F, perhaps T '＜T, this transfer process just is called interpolation.

The concrete steps of the method for high speed signal interpolation reconstruction are: a complete reconfiguration system to original analog bandlimited signal x (t) with sampling rate is $F=\frac{1}{T}$ Sampling pulse sample and obtain sequence x (n), when the expectation sample frequency of the output end signal y of system (n) is $F\′=\frac{1}{T\′}=\mathrm{LF},$ That is to say that system requirements improves L doubly to F ' time with sample frequency from original F, a plurality of zero point of equidistant insertion obtain new sequence m (n) between two adjacent actual samples points.Interpolation filter is to the frequency spectrum M (e of m (n) ^{J ω}) do low-pass filtering, isolate the base band component M ' (e of original signal ^{J ω}), again it being carried out inverse fourier transform, just can obtain original signal has been made signal after the interpolation of corresponding multiple, as shown in Figure 1.

At present, in the high-speed figure storage oscilloscope interpolation filter in order effectively to isolate the base band component of original signal, its frequency response H (e ^{J ω}) the approximate ideal low-pass filter, promptly $H\left(e^{\mathrm{j\&omega;}}\right)=\left\{\begin{array}{c}L,\left|\mathrm{\&omega;}\right|\&le;\mathrm{\&pi;}/\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="C200710121606E00123.png,C200710121606E00131.png"\; state="\{\{state\}\}">L</figure-callout>}\\ 0,\mathrm{else}\end{array}\right.,$ Its inverse fourier transform h (n) is: $h\left(n\right)=\frac{\sin \left[\mathrm{\&pi;}(n/L)\right]}{\mathrm{\&pi;}(n/L)},$ Its function waveform as shown in Figure 2.The sinusoidal interpolation filter that Here it is adopts at present usually.Though this interpolation filter is simple, effective, widespread use, in the experiment of high-speed data acquisition, can find to different input signals that sinusoidal interpolation algorithm can produce corresponding output distortion in various degree.For example when being input as square-wave signal, output can produce very significantly distortion, as shown in Figure 3.Fig. 3 shown to the input square wave carry out 4 times of reconstructed images that interpolation is later, as can be seen, output severe distortion has taken place, no longer be normal square wave.This distortion can cause the reduction greatly of measurement and display precision, and oscillographic design is unacceptable for high-speed wideband.

Summary of the invention

Problem at above-mentioned high speed signal interpolation reconstruction technology exists provides a kind of oscillographic high speed signal reconstruction method, can realize the purpose of high-quality reconstruct original signal.

Above-mentioned purpose of the present invention is achieved by following technical solution:

A kind of oscillographic high speed signal reconstruction method comprises: grandfather tape limited signal x (t) is sampled obtains sequence x (n), and a plurality of zero point of equidistant insertion obtain new sequence m (n) between two adjacent actual samples points; Utilize the frequency spectrum M (e of interpolation filter to m (n) ^{J ω}) carry out low-pass filtering, isolate the base band component X (e of original signal ^{J ω}); Base band component X (e to above-mentioned original signal ^{J ω}) carry out inverse fourier transform, obtain original signal has been made the later signal of interpolation, it is characterized in that, adopt the frequency domain sampling method to make up above-mentioned interpolation filter, promptly in frequency domain to ideal continuous frequency response sample, obtain its discrete series, described discrete series be weighted to revise obtain discrete sample value, above-mentioned discrete sample value is done inverse fourier transform, obtain the interpolation filter time domain sequences.

The continuous frequency response of described ideal is, the frequency response range value is 1 in the passband, and the frequency response range value is 0 in the stopband.

Adopt unit impulse function δ (t) to constitute the required cycle impulse function p (t) of sampling, to signal H _d(e ^{J ω}) sample, wherein sampling function is $p\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}(t-\mathrm{nT}).$

Adopt the Blackman window function that described discrete series is weighted correction,

N≤60 of described interpolation filter h (n).

Interpolation filter can be decomposed into multiphase filter ∑ h ' (n).Interpolation filter h (n) is decomposed into L subsequence: g ₀(n), g ₁(n) ..., g _L-1(n), above-mentioned subsequence is defined as subfilter: p _r(n)=g _r(n)=h (nL+r), wherein r ∈ (0,1,2 ..., L-1), L is the integer greater than 1.

Technological merit of the present invention is:

When with monolithic A/D input signal being carried out discrete sampling, the sampling interval of sequence is uniformly, is referred to as uniform sampling; And input signal being made up when sampling with multi-disc A/D, the sampling interval of sequence can be heterogeneous owing to deviation takes place not matching of parameter between the A/D, is referred to as nonuniform sampling.Interpolation filter is to make up at equal even non-homogeneous two kinds of sample sequences in the oscillographic high speed signal reconstruction method of the present invention, compares with traditional oscillographic high speed signal reconstruction method, and corrected spectrum is leaked the wave form distortion that is caused effectively.The physical features and the original signal of output signal fit like a glove, and have reached the purpose of high-quality reconstruct original signal.Simultaneously, because the reduction of operand has also significantly reduced system overhead, improved the system real time energy.Reached the purpose of high-quality reconstruct original signal.

Description of drawings

Fig. 1 is the digital interpolation system chart;

Fig. 2 is sinusoidal interpolating function synoptic diagram;

Fig. 3 be sinusoidal interpolation algorithm to square wave signal Processing design sketch, wherein, the original square-wave signal of Fig. 3 a input figure; The sinusoidal interpolation algorithm of Fig. 3 b is to four times of interpolation output maps of square-wave signal;

Fig. 4 is the ideal frequency response synoptic diagram of L times of interpolation filter;

Fig. 5 is (n) structural representation of ∑ h ' of multiphase filtering;

Fig. 6 is the design sketch of the present invention's offset of sinusoidal signal Processing in the hardware system of reality, wherein, and Fig. 6 a initial sinusoids signal input figure; Four times of interpolation output maps of the method offset of sinusoidal signal of Fig. 6 b high speed signal interpolation reconstruction of the present invention;

Fig. 7 is the present invention's design sketch to the square wave signal Processing in the hardware system of reality, wherein, and the original square-wave signal input of Fig. 7 a figure; Fig. 6 b revises the four times interpolation output maps of interpolation algorithm to square-wave signal.

Embodiment

Describe oscillographic high speed signal reconstruction method provided by the present invention in detail below in conjunction with accompanying drawing, but be not construed as limiting the invention.

Computer Simulation by interpolation filter and hardware system experiment, determining that the best of carrying out interpolative operation in high-speed data acquistion system counts is 60.The time domain impulse response of wave filter is unlimited in theory, and in engineering is used, can only use the finite length filtering device, so whole sampled values that can not the number of winning the confidence in the reality are carried out interpolation arithmetic, should be with the suitable compromise of counting, this has just introduced interpolated error.In frequency domain to continuous H _d(e ^{J ω}) when sampling, when sampled point was used greater than 60 somes calculating, its graph of errors had passed through flex point, increases sampling number again, interpolation error does not almost reduce.Consistent with the theoretical analysis result that adopts the fourier progression expanding method waveform.Therefore, take all factors into consideration the sum of errors computing cost, determine N≤60.The interpolation multiple of supposing the system is L, and the sequence x that obtains after the sampling (n) inserts after L-1 the null value, just obtains interpolation sequence M (n) later on.Frequency spectrum M (the e of M (n) ^{J ω}), be the frequency spectrum X (e of original series x (n) ^{J ω}) be compressed L doubly, M (e ^{J ω}) not only comprise X (e ^{J ω}) base band component, also comprised the mirror image of its high fdrequency component.For from M (e ^{J ω}) the middle fundamental frequency part X (e that extracts ^{J ω}), should carry out low-pass filtering to the sequence after the interpolation.

For the low-pass filter of a L times of interplotation system, in order effectively to isolate the base band component of original signal, its ideal frequency response H _d(e ^{J ω}) shown in 4 figure.In passband, H _d(e ^{J ω}) range value is 1; In stopband, its range value is 0.For constituting physically realizable wave filter, in the design of interpolation filter, adopt the frequency sampling method to make up wave filter.Frequency sampling method implementation method is simple, and calculated amount is moderate.That is, in frequency domain to the continuous frequency response H of ideal _d(e ^{J ω}) sample, to obtain its discrete series H _d(k).Constitute the required cycle impulse function p (t) of sampling with unit impulse function δ (t), to signal H _d(e ^{J ω}) sample, wherein sampling function is $p\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}(t-\mathrm{nT}).$ According to the Nyquist sampling theorem, handle continuous signal with digital form, do not need the value of infinite a plurality of points interior between action period, but only need limited the respective value on the sampling spot to get final product.Therefore, can be in twice sampling interval in front and back, the respective value of the signal that obtains is stored, so that carry out follow-up processing.As previously mentioned, in order to compensate and balance out the higher-order of oscillation that spectrum leakage causes, utilize the secondary lobe octave to decay faster window function to H _d(e ^{J ω}) discrete series H _d(k) each sample point is weighted correction, obtains discrete sample value H (k).Compare by Computer Simulation and real system operation result, select for use the Blackman window H _d(k) revise in the sample value of frequency field, obtain H (k).Discrete sample value H (k) is done inverse fourier transform, just obtain interpolation filter time domain sequences h (n), that is:

$h\left(n\right)\stackrel{\mathrm{IDFT}}{\&LeftArrow;}H\left(k\right)$

At this moment, h (n)=[0.0000 0.0001 0.0002 0.0002 0.0001-0.0001-0.0005-0.0007-0.0006-0.0003,0.0003 0.00080.0009,0.0005 0.0000 0.0004 0.0035 0.01210.0295,0.0594 0.1048 0.1674 0.3419 0.24730.5533,0.4463 0.6543 0.8028 0.7402 0.83580.8028,0.8358 0.7402 0.6543 0.5533 0.44630.3419,0.1674 0.2473 0.1048 0.0594 0.02950.0121,0.0035 0.0004 0.0005 0.0000 0.00090.0008 0.0003-0.0003-0.0006-0.0007-0.0005-0.00010.0001 0.0002 0.0001 0.0002 0.0000]

The present invention can also adopt Hamming window, Hanning window, Chebyshev window to H _d(e ^{J ω}) sampled value H _d(k) each sample point is weighted correction.

Always work on the higher sample frequency F ' for fear of low-pass filter h (n), making the inefficiency of system increases the requirement to rear end digital signal processing arithmetic capability, should use multiphase filtering structure (being called the multi-channel network structure again) to g _m(n) transform.

To low-pass filter h (n), it can be decomposed into L subsequence: g ₀(n), g ₁(n) ..., g _L-1(n).Constant wave filter when these subsequences are equivalent to the independent linearity of sample frequency F, they all work in previous lower sample frequency F.The above-mentioned subsequence of h (n) is defined as subfilter:

p _r(n)＝g _r(n)＝h(nL+r)

Wherein r ∈ (0,1,2 ..., L-1).The wave filter of following formula definition is called as multiphase filter, and it is based on the characteristic of periodic function and a kind of filter construction of designing.It all has L output sampled value for the x (n) of each input.Multiphase filter p _r(n) be h (n) according to L at interval extracting resulting subsequence, and the frequency response of prototype filter h (n) is similar to the perfect low pass characteristic.So, when the frequency response range of prototype filter exists $0\&le;\mathrm{\&omega;}\&le;\frac{\mathrm{\&pi;}}{L}$ The time, the frequency response range of multiphase filter is positioned at 0≤ω '≤π.Its course of work as shown in Figure 5.With resulting h (n), be decomposed into the resulting multinomial wave filter of multiphase filtering structure.

Fig. 6, Fig. 7 have shown that the present invention's offset of sinusoidal in the hardware system of reality is imported and the different output datas of square wave input.

Sinusoidal signal x (t) input through oscillograph sampling (sampling number=50), storage, show result such as Fig. 6 a of (demonstration count=50), resulting result shows the n '=n * L=200 that counts carry out the interpolation reconstruct of interpolation multiple L=4 through above-mentioned interpolation reconstructing method after shown in Fig. 6 b.

By last figure as seen, the same with traditional sinusoidal interpolation algorithm for the sinusoidal signal input with the correction interpolation method that this paper proposed, can obtain comparatively satisfied signal reconstruction.

When system input signal is square-wave signal x (t), through oscillograph sampling (sampling number=50), storage, show result such as Fig. 7 a of (demonstration count=50), resulting result shows the n '=n * L=200 that counts carry out the interpolation reconstruct of interpolation multiple L=4 through above-mentioned interpolation reconstructing method after shown in Fig. 7 b.

As seen, for the square-wave signal input, the correction interpolation method that this paper proposed is compared with traditional sinusoidal interpolation algorithm, and corrected spectrum is leaked the wave form distortion that is caused effectively.The physical features of output signal and original signal are coincide, and have overcome the distortion that is produced by sinusoidal algorithm, have reached the purpose of high-quality reconstruct original signal.Simultaneously, because the reduction of operand has also significantly reduced system overhead, improved the system real time energy.

More than by specific embodiment oscillographic high speed signal reconstruction method provided by the present invention has been described, it will be understood by those of skill in the art that in the scope that does not break away from essence of the present invention, can make certain deformation or modification to the present invention; Its preparation method also is not limited to disclosed content among the embodiment.

Claims (6)

1, a kind of oscillographic high speed signal reconstruction method comprises: grandfather tape limited signal x (t) is sampled obtains sequence x (n), and a plurality of zero point of equidistant insertion obtain new sequence m (n) between two adjacent actual samples points; Utilize the frequency spectrum M (e of interpolation filter to m (n) ^{J ω}) carry out low-pass filtering, isolate the base band component X (e of original signal ^{J ω}); Base band component X (e to above-mentioned original signal ^{J ω}) carry out inverse fourier transform, obtain original signal has been made the later signal of interpolation, it is characterized in that: adopt the frequency domain sampling method to make up above-mentioned interpolation filter, promptly in frequency domain to the continuous frequency response H of ideal _d(e ^{J ω}) sample, obtain its discrete series, described discrete series is weighted correction obtains discrete sample value, above-mentioned discrete sample value is done inverse fourier transform, obtain interpolation filter time domain sequences h (n).

2, oscillographic high speed signal reconstruction method as claimed in claim 1 is characterized in that: the continuous frequency response of described ideal is, the frequency response range value is 1 in the passband, and the frequency response range value is 0 in the stopband.

3, oscillographic high speed signal reconstruction method as claimed in claim 1 is characterized in that: adopt unit impulse function δ (t) to constitute the required cycle impulse function p (t) of sampling, to signal H _d(e ^{J ω}) sample, wherein sampling function is $p\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}(t-\mathrm{nT}).$

4, as claim 1 or 3 described oscillographic high speed signal reconstruction methods, it is characterized in that: adopt the Blackman window function that described discrete series is weighted correction.

5, oscillographic high speed signal reconstruction method as claimed in claim 3 is characterized in that: n≤60 of described interpolation filter time domain sequences h (n).

6, oscillographic high speed signal reconstruction method as claimed in claim 1 is characterized in that: the interpolation filter time domain sequences is decomposed into multiphase filter time domain sequences ∑ h ' (n), is about to interpolation filter time domain sequences h (n) and is decomposed into L subsequence: g ₀(n), g ₁(n) ..., g _L-1(n), above-mentioned subsequence is defined as subfilter: p _r(n)=g _r(n)=and h (nL+r), wherein (0, L-1), r is an integer to r ∈, and L is the integer greater than 1.

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