CN103984866A - Signal denoising method based on local mean value decomposition - Google Patents
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Abstract
The invention discloses a signal denoising method based on local mean value decomposition. The method comprises the steps that the local mean value decomposition is carried out on a noisy signal, amplitude thresholding filtering processing is carried out on the obtained product function (PF) component, and a real source signal is reconstructed, so that noises are omitted, comparison is carried out by means of a simulation experiment, and the effectiveness of an LMD-based signal denoising method is verified by a practical signal noise elimination experiment. According to the method, the noise jamming in observed signals is eliminated, the effectiveness of the LMD-based signal denoising method is verified by virtue of a series of simulation and experiments and through the comparison with the existing wavelet transform (WT)-based denoising method and an empirical mode decomposition (EMD)-based denoising method which appears in recent years, the method is simple, the advantages of the denoising effect which utilizes an LMD-based denoising algorithm are obvious, the combination property is better, the secondary exquisite denoising of the noisy signal is realized, and the noise elimination effect is good.
Description
Technical field
The invention belongs to the technical field of signal processing, relate in particular to a kind of signal antinoise method decomposing based on local average.
Background technology
Signal denoising is a problem receiving much concern in signal process field.If contain real source signal s (n) and noise contribution u (n) in a sensing observation signal x (n), if x (n)=s (n)+u (n), claims to contain additive noise in x (n); If x (n)=s (n) u (n), claims that u (n) is multiplicative noise.In most of situation, noise is all additivity, and multiplicative noise is processed conventionally more difficult, need special treatment technology, and in this patent, the noise of indication is additivity.
Signal antinoise method has a lot, and traditional have the time domain method of average and wavelet transformation (WT) method etc.Time domain average method hypothesis source signal s (n) is deterministic signal, is averaged to offset the impact of noise by the addition of a large amount of observation samples; WT base Denoising Algorithm is a kind of threshold value screening technique, applies more extensive.The method thinks that signals with noise x (n) is after wavelet transform (DWT), and its energy only concentrates in the Wavelet Component of a few high amplitude.Adopt the different threshold rules of getting, Wavelet Component is screened and then reconstruction signal, the order of eliminating to reach noise.Get threshold rule different, the WT base denoising method of formation is also different, " firmly " threshold value of such as standard or " soft " threshold method, translation invariant threshold method and the threshold method etc. of getting distributing based on Bayesian probability.At the end of last century, Huang etc. have proposed empirical mode decomposition (EMD) method, and Hilbert-Huang transform (HHT) technology forming thus, be used for solving non-linear, unstable signal problem analysis, in the various fields such as radar, biomedicine, laser-ultrasound and earthquake, mechanical engineering, be used widely.In EMD theoretical research, a very natural problem is suggested, in intrinsic mode functions (IMF) component obtaining at EMD, which IMFs mainly comprises source signal s (n) information, does is which IMFs mainly made up of noise u (n) composition? the further investigation of this problem is impelled to the appearance of multiple EMD base denoising method.It is worthy of note especially, Kopsinis and McLaughlin are subject to the inspiration of Wavelet Denoising Method principle, and that has set up multiple adaptation EMD characteristic gets threshold rule, and then has proposed improved EMD base denoising method.Compare with existing EMD base denoising method with traditional wavelet basis denoising, improve one's methods and obtained better denoising effect.In recent years, multidigit scholar is also according to the signal denoising demand facing in different application field, existing EMD base denoising method is improved from different perspectives, and the EMD bis-times that comprise the electrocardiosignal denoising of associating EMD and DWT, becomes envelope processing based on cosine signal decomposes the compacting of seismic signal noises and the time-domain windowed EMD base laser ultrasound signal denoising based on kurtosis test strategy etc.At present, the application of EMD base denoising method presents the trend of continuous expansion.But EMD technology self exists some defects, as end effect, mode aliasing etc., may affect the signal denoising performance of EMD based method.At present, there is self-defect in traditional signal antinoise method, affects the signal denoising performance of EMD based method, and denoising effect is poor.
Summary of the invention
The object of the embodiment of the present invention is to provide a kind of signal antinoise method decomposing based on local average, is intended to solve traditional signal antinoise method and has self-defect, affects the poor problem of signal denoising performance, denoising effect of EMD based method.
The embodiment of the present invention is to realize like this, the signal antinoise method decomposing based on local average, the method step comprises that signals with noise is carried out to local average to decompose, obtained long-pending function (PF) component is carried out to the validity that filtering processing, the real source signal of reconstruct are cancelled, contrasted, verify LMD base signal antinoise method by emulation experiment to realize noise;
Described decomposes and refers to that utilizing LMD algorithm to carry out local average to signals with noise decomposes signals with noise execution local average, LMD can be used for analyzing the dissimilar unstable signals such as vibration, acoustics, electrocardiogram equipment, magnetic resonance image (MRI) and seismic event, in essence, LMD is exactly the progressive process of isolating a FM signal from an amplitude-modulated signal, comprises three basic steps: the smoothing techniques of (1) original signal; (2) from original signal, deduct the signal after smoothing techniques; (3) the amplitude demodulation processing of estimating based on envelope.Through the base conditioning of LMD, an original signal x (t) can be decomposed into K long-pending function PFk (t), k=1, and 2,, K, is called for short PF component, and its reconstruction expression formula is
（1）
In formula, uk (t) is residual component.
Further, the PF component of gained is carried out to following Hilbert (Hilbert) conversion, can obtain
（2）
Instantaneous frequency (IF) calculating formula is
（3）
Wherein i (t)=arctan[Hi (t)/PFi (t)].
Thereby original signal x (t) can be expressed as following real part form
（4）
In formula,
for envelope component, also referred to as instantaneous amplitude (IA).Finally, jointly provided the time-frequency description of original signal x (t) by IF and IA;
Described long-pending function (PF) component to obtained carries out filtering processing and refers in LMD decomposable process, in order to obtain smooth local average and envelope function continuously, continuous threshold is being carried out on the basis of time shift weighting, local mean value and amplitude are carried out to moving average (Moving Averaging) smoothing techniques, in EMD decomposes, that extreme point is directly carried out to cubic spline interpolation matching, picked up signal upper, lower envelope line and then ask for its average to realize signal decomposition, the decomposable process of LMD meets the natural characteristic of signal, can more be stablized, accurate IF and IA decomposition result, obtain the more details feature of signal time-frequency distributions, can carry out more significant physics explaination to signal,
The real source signal of described reconstruct refers to AM/FM amplitude modulation/frequency modulation signal of emulation to realize noise cancellation
, wherein
=20Hz,
=200Hz,
=40Hz, signal sampling points N=2048, sample frequency Fs=2000Hz, the time domain waveform, amplitude spectrum and application EMD, the LMD that have provided respectively signal y (t) decompose the instantaneous frequency (IF) obtaining, simulate signal y (t) is mainly made up of 91.8Hz frequency and integer frequency composition thereof, application LMD decomposition only obtains an IF component, but the actual frequency of having described preferably signal forms and situation of change, referring to the average frequency (Hz) shown in Fig. 2 b, for example 91.8,183.6,367.2 and 734.4 etc.EMD extracts five IF components altogether, can obviously see that its waveform presents irregular big ups and downs,, is difficult to the formation of signal to make rational physical interpretation without obvious corresponding relation with the actual component frequency of signal y (t);
Described contrasts and refers to emulation " Doppler " respectively by emulation experiment, " Blocks ", " Bumps " and sine wave be totally four class source signal si (t), i=1 ~ 4, by adding white Gaussian noise in various degree, can obtain the observation xi (t) that makes an uproar of the band with different signal to noise ratio (snr)s, i=1 ~ 4, regulate and get threshold operation and source signal process of reconstruction by change M1 and IM2 parameter, meet and be related to M2=K-IM2, wherein K is the sum of PF component, in emulation, EMD base denoise algorithm is preferably sieved number of times and is fixed as 8 times, get threshold operation and source signal reconstruction parameter M1=3, IM2=2, in LMD base denoise algorithm, be set to M1=1, IM2=1.Constant C is all set to C=0.7 in two kinds of algorithms, adopts different simulation parameter settings, and the denoising performance obtaining is also different;
The denoising result (SNR2) that the validity of described checking LMD base signal antinoise method refers to EMD and LMD base algorithm gained along with band make an uproar observation signal signal to noise ratio (S/N ratio) (SNR1) variation and change, for " Doppler " and " Blocks " class signal, for example, in the time that observation signal to noise ratio (S/N ratio) (about SNR1 < 13dB) is lower, adopt behaving oneself best of the rigid EMD base denoise algorithm EMD-H that gets threshold treatment, in the time that SNR1 further increases, the denoising performance of LMD base algorithm (comprising LMD-H and LMD-S) has surmounted EMD base algorithm in succession, for " Sin " class signal, surmounting of this performance advanceed to SNR1 4dB left and right, for " Bumps " class signal, the performance of algorithm EMD-H is best always, next is LMD-H algorithm, two kinds of algorithms of LMD-S and EMD-S are substantially suitable to the denoising performance of this type of signal, and for all four class simulate signals, same denoise algorithm is as WT, EMD or LMD adopt hard threshold processing (H) generally better than the denoising effect of flexible thresholding processing (S), in emulation, also find: during from SNR1 > 3dB, the denoising performance of EMD base algorithm just starts to reduce, along with the increase hydraulic performance decline trend of SNR1 is obvious, contrary with EMD base algorithm, LMD base algorithm improves constantly the denoising performance of emulation Sin signal, particularly adopts the LMD-H of hard threshold processing.
Further, the described signal antinoise method decomposing based on local average is in many practical application, to be difficult to obtain real source signal s and noise component n, but conventionally can obtain being with the observation signal x that makes an uproar, for the different denoise algorithm of comparison test, designed denoising experimental provision, this experimental provision is made up of standard signal generator, digital oscilloscope and AVANT integrated data acquisition instrument, and experimental procedure is as follows:
(1) connect signal generator and oscillograph, adjusting and producing an amplitude is the standard square-wave signal that A, frequency are f;
(2) this signal is inputted in the first passage " CH1 " of eight channel data Acquisition Instruments, other passages are vacant, gather digital signal.Consider that the high frequency noise that may exist in data acquisition system (DAS) disturbs, in experiment, having set higher sample frequency is Fs=48kHz;
(3) from virtual band make an uproar intercept arbitrarily square wave observation signal x (t) one section complete cycle sample, be designated as without loss of generality x;
(4), from the known band observation sample x that makes an uproar, according to the square-wave signal of experiment parameter (A, f and Fs etc.) structure one approximate " pure ", be designated as s.Utilize this reference source signal s, can approximate treatment observe signal to noise ratio snr 1, and investigate the denoising performance of comparison algorithms of different according to the signal to noise ratio snr 2 after denoising.
Effect gathers
The signal antinoise method decomposing based on local average provided by the invention, eliminate the noise in observation signal, by a series of emulation and experiment, by with existing signal antinoise method based on wavelet transformation (WT) and the signal antinoise method based on empirical mode decomposition (EMD) occurring in recent years contrast, verified the validity of the LMD base signal antinoise method proposing.The signal antinoise method that decomposes based on local average is simple, utilize the denoising effect of LMD base denoise algorithm with the obvious advantage, has good combination property, and signals with noise is carried out to the meticulous denoising of secondary, effective.
Brief description of the drawings
Fig. 1 is the flow chart of steps of signal antinoise method of decomposing based on local average that the embodiment of the present invention provides.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.
Below in conjunction with drawings and the specific embodiments, application principle of the present invention is further described.
As shown in Figure 1, the signal antinoise method decomposing based on local average, the method step comprises that signals with noise is carried out to local average to decompose S101, obtained long-pending function (PF) component is carried out to the validity S105 that filtering treatment S 102, the real source signal of reconstruct are cancelled S103, contrasted S104, checking LMD base signal antinoise method by emulation experiment to realize noise;
Described refers to that to signals with noise execution local average decomposition S101 utilizing LMD algorithm to carry out local average to signals with noise decomposes, LMD can be used for analyzing the dissimilar unstable signals such as vibration, acoustics, electrocardiogram equipment, magnetic resonance image (MRI) and seismic event, in essence, LMD is exactly the progressive process of isolating a FM signal from an amplitude-modulated signal, comprises three basic steps: the smoothing techniques of (1) original signal; (2) from original signal, deduct the signal after smoothing techniques; (3) the amplitude demodulation processing of estimating based on envelope, through the base conditioning of LMD, an original signal x (t) can be decomposed into K long-pending function PFk (t), k=1,2,, K, is called for short PF component, and its reconstruction expression formula is
（1）
In formula, uk (t) is residual component.
Further, the PF component of gained is carried out to following Hilbert (Hilbert) conversion, can obtain
（2）
Instantaneous frequency (IF) calculating formula is
（3）
Wherein i (t)=arctan[Hi (t)/PFi (t)].
Thereby original signal x (t) can be expressed as following real part form
（4）
In formula,
for envelope component, also referred to as instantaneous amplitude (IA).Finally, jointly provided the time-frequency description of original signal x (t) by IF and IA;
Described long-pending function (PF) component to obtained carries out filtering treatment S 102 and refers in LMD decomposable process, in order to obtain smooth local average and envelope function continuously, continuous threshold is being carried out on the basis of time shift weighting, local mean value and amplitude are carried out to moving average (Moving Averaging) smoothing techniques, in EMD decomposes, that extreme point is directly carried out to cubic spline interpolation matching, picked up signal upper, lower envelope line and then ask for its average to realize signal decomposition, the decomposable process of LMD meets the natural characteristic of signal, can more be stablized, accurate IF and IA decomposition result, obtain the more details feature of signal time-frequency distributions, can carry out more significant physics explaination to signal,
The real source signal of described reconstruct refers to AM/FM amplitude modulation/frequency modulation signal of emulation to realize noise cancellation S103
, wherein
=20Hz,
=200Hz,
=40Hz, signal sampling points N=2048, sample frequency Fs=2000Hz, the time domain waveform, amplitude spectrum and application EMD, the LMD that have provided respectively signal y (t) decompose the instantaneous frequency (IF) obtaining, simulate signal y (t) is mainly made up of 91.8Hz frequency and integer frequency composition thereof, application LMD decomposition only obtains an IF component, but has described preferably actual frequency formation and the situation of change thereof of signal.EMD extracts five IF components altogether, can obviously see that its waveform presents irregular big ups and downs,, is difficult to the formation of signal to make rational physical interpretation without obvious corresponding relation with the actual component frequency of signal y (t);
Described contrast S104 by emulation experiment and refer to emulation " Doppler " respectively, " Blocks ", " Bumps " and sine wave be totally four class source signal si (t), i=1 ~ 4, by adding white Gaussian noise in various degree, can obtain the observation xi (t) that makes an uproar of the band with different signal to noise ratio (snr)s, i=1 ~ 4, regulate and get threshold operation and source signal process of reconstruction by change M1 and IM2 parameter, meet and be related to M2=K-IM2, wherein K is the sum of PF component, in emulation, EMD base denoise algorithm is preferably sieved number of times and is fixed as 8 times, get threshold operation and source signal reconstruction parameter M1=3, IM2=2, in LMD base denoise algorithm, be set to M1=1, IM2=1, constant C is all set to C=0.7 in two kinds of algorithms, adopts different simulation parameter settings, and the denoising performance obtaining is also different,
The denoising result (SNR2) that the validity S105 of described checking LMD base signal antinoise method refers to EMD and LMD base algorithm gained along with band make an uproar observation signal signal to noise ratio (S/N ratio) (SNR1) variation and change, for " Doppler " and " Blocks " class signal, for example, in the time that observation signal to noise ratio (S/N ratio) (about SNR1 < 13dB) is lower, adopt behaving oneself best of the rigid EMD base denoise algorithm EMD-H that gets threshold treatment, in the time that SNR1 further increases, the denoising performance of LMD base algorithm (comprising LMD-H and LMD-S) has surmounted EMD base algorithm in succession, for " Sin " class signal, surmounting of this performance advanceed to SNR1 4dB left and right, for " Bumps " class signal, the performance of algorithm EMD-H is best always, next is LMD-H algorithm, two kinds of algorithms of LMD-S and EMD-S are substantially suitable to the denoising performance of this type of signal, and for all four class simulate signals, same denoise algorithm is as WT, EMD or LMD adopt hard threshold processing (H) generally better than the denoising effect of flexible thresholding processing (S), in emulation, also find: during from SNR1 > 3dB, the denoising performance of EMD base algorithm just starts to reduce, along with the increase hydraulic performance decline trend of SNR1 is obvious, contrary with EMD base algorithm, LMD base algorithm improves constantly the denoising performance of emulation Sin signal, particularly adopts the LMD-H of hard threshold processing.
Further, the described signal antinoise method decomposing based on local average is in many practical application, to be difficult to obtain real source signal s and noise component n, but conventionally can obtain being with the observation signal x that makes an uproar, for the different denoise algorithm of comparison test, designed denoising experimental provision, this experimental provision is made up of standard signal generator, digital oscilloscope and AVANT integrated data acquisition instrument, and experimental procedure is as follows:
(1) connect signal generator and oscillograph, adjusting and producing an amplitude is the standard square-wave signal that A, frequency are f;
(2) this signal is inputted in the first passage " CH1 " of eight channel data Acquisition Instruments, other passages are vacant, gather digital signal.Consider that the high frequency noise that may exist in data acquisition system (DAS) disturbs, in experiment, having set higher sample frequency is Fs=48kHz;
(3) from virtual band make an uproar intercept arbitrarily square wave observation signal x (t) one section complete cycle sample, be designated as without loss of generality x;
(4), from the known band observation sample x that makes an uproar, according to the square-wave signal of experiment parameter (A, f and Fs etc.) structure one approximate " pure ", be designated as s.Utilize this reference source signal s, can approximate treatment observe signal to noise ratio snr 1, and investigate the denoising performance of comparison algorithms of different according to the signal to noise ratio snr 2 after denoising.
Principle of work
As shown in Figure 1, a kind of signal antinoise method technological process of decomposing based on local average comprises that signals with noise is carried out to local average to decompose S101, obtained long-pending function (PF) component is carried out to the validity S105 that filtering treatment S 102, the real source signal of reconstruct are cancelled S103, contrasted S104, checking LMD base signal antinoise method by emulation experiment to realize noise; The signal antinoise method decomposing based on local average, eliminate the noise in observation signal, by a series of emulation and experiment, by with existing signal antinoise method based on wavelet transformation (WT) and the signal antinoise method based on empirical mode decomposition (EMD) occurring in recent years contrast, verify the validity of the LMD base signal antinoise method proposing, method is simple, utilize the denoising effect of LMD base denoise algorithm with the obvious advantage, there is good combination property, signals with noise is carried out to the meticulous denoising of secondary, effective.
The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any amendments of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.
Claims (2)
1. the signal antinoise method decomposing based on local average, it is characterized in that, the method step comprises carries out to signals with noise the validity that local average is decomposed, obtained long-pending function (PF) component carried out amplitude thresholds filtering processing, the real source signal of reconstruct and cancels to realize noise, contrasts, eliminates by actual signal noise by emulation experiment experimental verification LMD base signal antinoise method;
Described decomposes and refers to that utilizing LMD algorithm to carry out local average to signals with noise decomposes signals with noise execution local average, LMD can be used for analyzing the dissimilar unstable signals such as vibration, acoustics, electrocardiogram equipment, magnetic resonance image (MRI) and seismic event, in essence, LMD is exactly the progressive process of isolating a FM signal from an amplitude-modulated signal, comprises three basic steps: the smoothing techniques of (1) original signal; (2) from original signal, deduct the signal after smoothing techniques; (3) the amplitude demodulation processing of estimating based on envelope; Through the base conditioning of LMD, an original signal x (t) can be decomposed into K long-pending function PFk (t), k=1, and 2,, K, is called for short PF component, and its reconstruction expression formula is
（1）
In formula, uk (t) is residual component;
Further, the PF component of gained is carried out to following Hilbert (Hilbert) conversion, can obtain
（2）
Instantaneous frequency (IF) calculating formula is
（3）
Wherein i (t)=arctan[Hi (t)/PFi (t)];
Thereby original signal x (t) can be expressed as following real part form
（4）
In formula,
for envelope component, also referred to as instantaneous amplitude (IA);
Finally, jointly provided the time-frequency description of original signal x (t) by IF and IA;
Described long-pending function (PF) component to obtained carries out amplitude thresholds filtering processing and refers to signals with noise is carried out to interval threshold processing through the PF component of LMD gained, right
mthe individual expectation band PF component of making an uproar
pF m (
t),
m=1,2,,
m, carry out filtering processing according to getting below threshold rule;
(i) threshold (HIT) is got at rigid interval:
(1)
(ii) flexible spacer is got threshold (SIT):
(2)
In formula (1) and (2),
z j (
i)
=[
w j (
i)
w j+ 1
(
i)
],
i=1,2,,
m,
j=1,2,,
n z (
i)
be
ithe make an uproar zero crossing interval of PF component of individual expectation band, wherein
n z (
i)
for interval
z j (
i)
number,
w j (
i)
with
w j+ 1
(
i)
for interval endpoint;
p (
i)
(
r j (
i)
) be the extreme value of wayside signaling, wherein
r j (
i)
for interval extreme point;
p (
i)
(
z j (
i)
),
p tO (
i)
(
z j (
i)
) be respectively thresholding and process forward and backward
ithe make an uproar interval function value of PF component of individual expectation band;
Noise-removed threshold value
t i as follows:
(3)
In formula,
cfor constant;
e i be
ithe energy of individual " pure " noise PF component, can be estimated by following formula:
(4)
In formula,
e 1 2the energy of the 1st PF component extracting for LMD;
For some specific LMD processing procedures, parameter
rwith
bdepend primarily on the iterations of LMD decomposable process;
The real source signal of described reconstruct is cancelled and is referred to according to following formula and carry out source signal to realize noise
s(
t) reconstruction, and then realize noise in grandfather tape noise cancellation signal and eliminate;
(1)
In formula (1),
m=
m 2-
m 1+ 1,
mfor expecting to be with the number of the PF component of making an uproar;
By introducing parameter
m 1with
m 2, can regulate the dirigibility of PF threshold filter and source signal process of reconstruction;
Described contrasts and refers to emulation " Doppler " respectively by emulation experiment, " Blocks ", " Bumps " and sine wave be totally four class source signal si (t), i=1 ~ 4, by adding white Gaussian noise in various degree, can obtain the observation xi (t) that makes an uproar of the band with different signal to noise ratio (snr)s, i=1 ~ 4, regulate and get threshold operation and source signal process of reconstruction by change M1 and IM2 parameter, meet and be related to M2=K-IM2, wherein K is the sum of PF component, in emulation, EMD base denoise algorithm is preferably sieved number of times and is fixed as 8 times, get threshold operation and source signal reconstruction parameter M1=3, IM2=2, in LMD base denoise algorithm, be set to M1=1, IM2=1, constant C is all set to C=0.7 in two kinds of algorithms, adopts different simulation parameter settings, and the denoising performance obtaining is also different,
The described actual signal noise that passes through is eliminated denoising result (SNR2) that the validity of experimental verification LMD base signal antinoise method refers to EMD and LMD base algorithm gained along with the make an uproar variation of signal to noise ratio (S/N ratio) (SNR1) of observation signal of band changes, for " Doppler " and " Blocks " class signal, for example, in the time that observation signal to noise ratio (S/N ratio) (about SNR1 < 13dB) is lower, adopt behaving oneself best of the rigid EMD base denoise algorithm EMD-H that gets threshold treatment, in the time that SNR1 further increases, the denoising performance of LMD base algorithm (comprising LMD-H and LMD-S) has surmounted EMD base algorithm in succession, for " Sin " class signal, surmounting of this performance advanceed to SNR1 4dB left and right, for " Bumps " class signal, the performance of algorithm EMD-H is best always, next is LMD-H algorithm, two kinds of algorithms of LMD-S and EMD-S are substantially suitable to the denoising performance of this type of signal, and for all four class simulate signals, same denoise algorithm is as WT, EMD or LMD adopt hard threshold processing (H) generally better than the denoising effect of flexible thresholding processing (S), in emulation, also find: during from SNR1 > 3dB, the denoising performance of EMD base algorithm just starts to reduce, along with the increase hydraulic performance decline trend of SNR1 is obvious, contrary with EMD base algorithm, LMD base algorithm improves constantly the denoising performance of emulation Sin signal, particularly adopts the LMD-H of hard threshold processing.
2. the signal antinoise method decomposing based on local average as claimed in claim 1, it is characterized in that, the described signal antinoise method decomposing based on local average is in many practical application, to be difficult to obtain real source signal s and noise component n, but conventionally can obtain being with the observation signal x that makes an uproar, for the different denoise algorithm of comparison test, design denoising experimental provision, this experimental provision is made up of standard signal generator, digital oscilloscope and AVANT integrated data acquisition instrument, and experimental procedure is as follows:
(1) connect signal generator and oscillograph, adjusting and producing an amplitude is the standard square-wave signal that A, frequency are f;
(2) this signal is inputted in the first passage " CH1 " of eight channel data Acquisition Instruments, other passages are vacant, gather digital signal;
Consider that the high frequency noise that may exist in data acquisition system (DAS) disturbs, in experiment, having set higher sample frequency is Fs=48kHz;
(3) from virtual band make an uproar intercept arbitrarily square wave observation signal x (t) one section complete cycle sample, be designated as without loss of generality x;
(4), from the known band observation sample x that makes an uproar, according to the square-wave signal of experiment parameter (A, f and Fs etc.) structure one approximate " pure ", be designated as s;
Utilize this reference source signal s, can approximate treatment observe signal to noise ratio snr 1, and investigate the denoising performance of comparison algorithms of different according to the signal to noise ratio snr 2 after denoising.
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