CN100596061C - Method for watermarking small wave threshold digital audio multiple mesh based on blind source separation - Google Patents

Abstract

The invention is concerned with compose method of robust watermark and fragile watermark in the multimedia information safety technology field, especially of the production of robust watermark and fragile watermark, inset, pick-up and juggle detecting method of watermark. Using the instantaneous mixing model of blind source separation, the robust watermark and fragile watermark with large mount ofinformation inset into originality audio frequency signal in arbitrary sequence, and the accurate orientation of juggle reflects the wave of signal to originality audio frequency data. It opens multi-objective inset, pick-up and juggle detecting method of watermark, and the safety of watermark depends on the encryption key information. Input the robust watermark and fragile watermark to the audiofrequency production at the same time to protect the copyright and local the juggle. Because the inset of robust watermark and fragile watermark is in arbitrary sequence without the restriction of inset order, without keeping secret and pick-up arithmetic, it reduces the difficulty of arithmetic.

Description

A kind of method for watermarking small wave threshold digital audio multiple mesh that separates based on blind source

Technical field

The invention belongs to the multi-media information security technical field, relate to the integrated method of robust watermarking and fragile watermark, the particularly generation of robust watermarking and fragile watermark, the embedding of watermark, extraction and altering detecting method.

Background technology

At present, the research major part about digital audio frequency watermark concentrates on the robust watermarking of realizing copyright protection or the fragile watermark of the realizing the content integrity authentication.Yet need realize the purpose of copyright protection and tampering location simultaneously in many applications.Robust watermarking can carry out copyright protection to audio product; Fragile watermark can be realized the tampering location of audio product.The two being integrated, on the basis that requires algorithm simply and not to need to consider robust watermarking and fragile watermark embedding order, both can realize blind Detecting, can disclose watermarking algorithm again, is a difficult point that realizes the watermark of many purposes.

Up to now, in audio signal, embed robust watermarking and fragile watermark, many purposes water mark method of realizing copyright protection and tampering location simultaneously mainly contains following three kinds: 1) calendar year 2001, Lu C S and Liao H Y M deliver on IEEE Transactions onImage Processing periodical " Multipurpose watermarking for image authenticationand protection paper; propose a kind of many purposes watermark embedding method in the literary composition; this method adopts different watermark detection process to robust watermarking with fragile watermark; it can realize the blind Detecting and the tampering location of watermark based on the cocktail party principle; but belong to 1 bit information on the embedded robust watermarking Essence of Information in this method, there is not specific concrete implication; 2) 2005, Wang R D, Xu D W and Li Q deliver in International Conference on Machine Learning andCybernetics international conference " Multiple audio watermarks based on lifting wavelettransform paper; propose a kind of many purposes water mark method in the literary composition; this method is finished the telescopiny of watermark by quantizing the Lifting Wavelet coefficient in wavelet field; it can realize the blind Detecting of watermark based on Lifting Wavelet and quantification; but fragile watermark only can be used for the integrality of confirmatory message, and can not realize tampering location; 3) 2005, Takahashi A, Nishimura R and Suzuki Y deliver on IEEE Transactions on Signal Processing periodical " Multiple watermarks for stereo audio signals using phase-modulation techniques paper; propose a kind of many purposes water mark method in the literary composition; this method realizes the extraction of watermark by means of short time discrete Fourier transform, and leaching process needs original audio signal based on frequency division multiplexing and phase modulated.

The theoretical foundation that watermark embeds and extracts among the present invention is blind source separation theorem.Linear, instantaneous, muting blind source separation problem can be described with following mixed equation

X＝AS(1)

In the formula, S=[S ₁, S ₂..., S _N] ^TBe the N dimensional vector that N source signal constitutes, X=[X ₁, X ₂..., X _M] ^TBe M dimension observation data vector, the output of corresponding each transducer of its element, M * N dimension matrix A be called hybrid matrix (generally suppose N≤M), its element representation the mixing situation of source signal.The implication of formula (1) is that N source signal obtains M dimension observation data vector by hybrid matrix A.The problem that solves is separated in blind source: under hybrid matrix A and source signal S condition of unknown, only determine separation matrix W according to observation data vector X, make output after the conversion

Be copy or the estimation of source signal vector S, and

In each component

Separate as much as possible.

Existing blind source separation algorithm roughly can be divided into three major types: independent component analysis method, entropy maximization method and non-linear principal component method.

Summary of the invention

The objective of the invention is by means of blind source separation theorem, a kind of method that embeds robust watermarking and fragile watermark in the wavelet coefficient of audio signal simultaneously is provided, solve relevant with fragile watermark embedding order in existing many purposes watermarking project with robust watermarking, the robust watermarking amount of information is little, embedding and extracting method complexity and watermark fail safe depend on watermark embedding and extracting method problem.

Technical scheme of the present invention is as follows: establishing the original digital audio signal is S={s (i), 1≤i≤L}, and wherein LL is the number of data points of audio signal, s (i) ∈ 0,1 ..., 2 ³-1} is the range value of i data point of audio signal, and b is the employed bit number of each audio signal data of expression.

If robust watermarking be bianry image W={w (i, j), 1≤i≤P, 1≤j≤Q} wherein w (P and Q are respectively the line number and the columns of watermarking images for i, the j) gray value of capable, the j row pixel of expression robust watermarking image i.If fragile watermark W _fBe the chaos sequence that produces by specific initial value.

One, the telescopiny of digital watermarking

The telescopiny of robust watermarking and fragile watermark is as follows respectively:

(1) telescopiny of Robust digital figure watermark

(1) preliminary treatment of digital figure watermark

At first, binary bitmap is carried out dimension-reduction treatment, the gray value that is about to its each pixel is end to end by row, formation is remained unchanged 1 in this sequence by 0 and 1 one-dimensional sequence that constitutes again, and 0 usefulness-1 is replaced, obtain by-1 and 1 sequence W ' that constitutes={ w ' (k), 1≤k≤P * Q}; Then, with chaos sequence W ' is carried out scrambling encryption at random, concrete grammar is: generate the chaos sequence with length with W ' by key I1, readjust the middle positions of elements of W ' according to chaos sequence, form robust watermarking sequence W to be embedded _r={ w _r(k), 1≤k≤P * Q}.

(2) Haar wavelet transformation and wavelet coefficient chooses

Use the Haar small echo original audio signal is carried out three grades of wavelet decomposition, what obtain third level small echo approaches component cA ³With details component cD3.The cA3 component is divided into some frames of equal length, and the length of every frame should be less than the length P that treats embedding robust watermarking signal * Q.Select the bigger coefficient of range value in every frame and constitute sequence S _r={ simultaneously, the positional information that writes down the big coefficient of range value in every frame keeps as key key1 for sr (k), 1≤k≤P * Q}.

(3) embedding of robust watermarking

Watermark embed process utilizes the instantaneous mixed model in the separation theorem of blind source to finish.Sequence S _rAs a source in the source signal mixing, another source is robust watermarking sequence W to be embedded _rThe telescopiny of robust watermarking can be described with formula (2): (2)

$X_r=\left[\begin{array}{c}{S}_{\mathrm{Wr}1}\\ {\mathrm{<figure-callout\; id="2"\; label="S\; Wr"\; filenames="C2006102000260011H1.png,C2006102000260011H3.png"\; state="\{\{state\}\}">S</figure-callout>}}_{\mathrm{Wr}}\end{array}\right]=A_r\&CenterDot;S_r=\left[\begin{array}{cc}{a}_{r11}& a_{r12}\\ a_{r21}& a_{r22}\end{array}\right]\&CenterDot;\left[\begin{array}{c}{S}_r\\ W_r\end{array}\right]$

In the formula, hybrid matrix A _rBe a non-singular matrix, in order to guarantee the transparency of algorithm, a _R11Should be much larger than a _R12, a _R21Much larger than a _R22, S _Wr1And S _Wr2Be the wavelet coefficient behind the embedding robust watermarking, wherein one tunnel coefficient S _Wr2Keep another road coefficient S as key key2 _Wr1Replace the cA3 coefficient of correspondence position.

(2) telescopiny of fragile watermark

The telescopiny and the robust watermarking of fragile watermark are basic identical, and different is to embed choosing of coefficient selection and hybrid matrix coefficient.In order to reduce the key information of reservation, the details component cD3 of original audio signal wavelet coefficient is proceeded the two-stage wavelet decomposition, obtain it and approach component cD3 _A2, be designated as S _fThe number of times that need to prove decomposition is many more, and the key length of required reservation is short more, but the operand that is consumed is also just big more.Need on the basis of taking all factors into consideration key length and operand, make a compromise selection.By key I ₂Generate and S _fAs fragile watermark sequence to be embedded, be designated as W with the chaos sequence of length _fWatermark embed process still utilizes the instantaneous mixed model in the separation theorem of blind source to finish.Sequence S _fAs a source in the source signal mixing, another source is fragile watermark sequence W to be embedded _fThe telescopiny of fragile watermark can be described with formula (3):

$X_f=\left(\begin{array}{c}{S}_{\mathrm{Wf}1}\\ {\mathrm{<figure-callout\; id="2"\; label="S\; Wf"\; filenames="C2006102000260011H1.png,C2006102000260011H3.png"\; state="\{\{state\}\}">S</figure-callout>}}_{\mathrm{Wf}}\end{array}\right)=A_f\&CenterDot;S_f=\left(\begin{array}{cc}{a}_{f11}& a_{f12}\\ a_{f21}& a_{f22}\end{array}\right)\&CenterDot;\left(\begin{array}{c}{S}_f\\ W_f\end{array}\right)$ (3)

In the formula, hybrid matrix A _fBe a non-singular matrix, the same transparency, a in order to ensure algorithm _F11Should be much larger than a _F12, a _F21Much larger than a _F22, S _Wf1And S _Wf2Be the coefficient behind the embedding fragile watermark, wherein one tunnel coefficient S _Wf2Keep another road coefficient S as key key3 _Wf1Replace original cD3 _A2Coefficient is as the cD3 after watermarked _A2Coefficient.

Finish after the aforesaid operations, the wavelet coefficient after will handling through water mark inlaying carries out inverse wavelet transform together in conjunction with not selected wavelet coefficient, can obtain to embed the audio signal of robust watermarking and fragile watermark.

Two, the extraction of digital watermarking and distort testing process

The leaching process of watermark is the inverse process that watermark embeds, and can utilize the general separation algorithm in the separation theorem of blind source to finish.The extraction of robust watermarking and fragile watermark and to distort testing process respectively as follows:

(1) leaching process of Robust digital figure watermark

Watermark may be contained in the audio signal to be detected, also watermark information may be do not contained; May pass through attack, also may not pass through any attack,, audio signal to be detected has been designated as S ' for showing difference.Use the haar small echo S ' is carried out three grades of wavelet decomposition, what obtain third level small echo approaches component cA3 ' and details component cD3 '.The location key information key1 that is kept when embedding with watermark selects the wavelet coefficient that has embedded watermark, is designated as S _Wr1', with the road key information key2 (S that keeps _Wr2) together as the two-way observation signal, utilize a kind of blind source separation method that both are separated, obtain W _rAnd S _rEstimated value

With

Because intrinsic randomness is separated in blind source, so and do not know which is in the isolated two paths of signals

Which is

Because audio signal and image sequence take on a different character, can distinguish isolated two paths of signals and judge by means of the quadravalence statistic.With sequence

In each element be that threshold value is carried out binary conversion treatment with zero, obtain by-1 and 1 sequence that constitutes, through being inverted unrest and inverse mapping, obtain, through rising after dimension handles the robust watermarking image that can obtain extracting by 0 and 1 binary sequence that constitutes

(2) extraction of fragile watermark and distort testing process

Carrying out before fragile watermark extracts, three grades of small echo details component cD3 ' of audio signal to be detected are further being carried out the two-stage wavelet decomposition, obtaining it and approach component cD3 _A2', be designated as S _Wf1'.Check cD3 _A2' length whether consistent with the length of key information key3, if both length is inconsistent, illustrate that audio-frequency information is modified, no longer safe and reliable, do not carry out the extraction of fragile watermark; If both length is identical, then proceed the extraction of fragile watermark.With S _Wf1' with the road key information key3 (S that keeps _Wf2) together as the two-way observation signal, utilize a kind of blind source separation method that the two is separated, obtain W _fAnd S _fEstimated value

With

By detecting

With

Quadravalence statistics value, can judge audio signal and whether be distorted.

With

Between coefficient correlation can utilize formula (4) to calculate:

${\mathrm{\&rho;}}_{W_f{\hat{W}}_f}=\left[\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{W}_f\left(k\right){\hat{W}}_f\left(k\right)\right]/{\left[\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|W_f\left(k\right)\right|}^2\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|{\hat{W}}_f\left(k\right)\right|}^2\right]}^{1/2},k=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,K---\left(4\right)$

Wherein, K is the length of the used key information key3 in front.With W _fWith Between coefficient correlation

Compare (as the formula (5)) with prior preset threshold th1 th1

$\mathrm{check}=\left\{\begin{array}{cc}1,& \left|{\mathrm{\&rho;}}_{W_f{\hat{W}}_f}\right|\&GreaterEqual;\mathrm{<figure-callout\; id="1"\; label="th"\; filenames="C2006102000260011H3.png,C2006102000260012H4.png"\; state="\{\{state\}\}">th</figure-callout>}1\\ 0,& \mathrm{else}\end{array}\right.---\left(5\right)$

If check=1, the content that audio signal to be detected then is described is safe, does not carry out any processing of distorting or resample; If check=C, audio signal then to be detected has been distorted or has been passed through to resample and handled.To handle two kinds of situations in order further distinguishing to distort and resample, need to judge by means of prior preset threshold th2.If isolated two paths of signals

With In the value of road signal quadravalence statistic greater than th2, think that then audio signal is distorted, extract corresponding to this road signal of this quadravalence statistic

With

As cD3 _A2' coefficient, other wavelet coefficient null representation, through after the wavelet inverse transformation, the time domain waveform figure of formation has reflected the situation of distorting for the treatment of detection signal.At this moment among the domain waveform figure, the zone that amplitude is concentrated more a little louder the is corresponding position of being distorted, and can roughly reflect the time domain waveform of the signal that is used to replace original audio data.Otherwise, think that this audio signal has been passed through resample to handle.

Effect of the present invention and benefit are to adopt the method that embeds robust watermarking and fragile watermark in audio product simultaneously, the purpose of realization copyright protection and tampering location.Because robust watermarking and fragile watermark can carry out according to random order when embedding, and are not embedded the constraint of order, not need to be keep secret embedding and extraction algorithm, thereby reduced the difficulty of algorithm.The present invention not only can realize copyright protection; and can realize tampering location, and can be widely used in both having needed to carry out copyright protection, need to carry out the situation of tampering location again; as public security, fire-fighting and judicial department's witness' evidence, and the audio frequency media data on the network etc.

Description of drawings

Fig. 1 is the theory diagram that watermark of the present invention embeds.

Fig. 2 is watermark extracting of the present invention and distorts the theory diagram of detection.

Fig. 3 (a) original digital audio time domain plethysmographic signal figure.

Fig. 3 (b) embeds the digital audio and video signals time domain waveform figure of robust watermarking and fragile watermark.

The original robust watermarking image of Fig. 3 (c).

The robust watermarking image that Fig. 3 (d) does not extract under fire the time.

The robust watermarking image that extracts during Fig. 3 (e) wrong cipher key.

The watermarked digital audio and video signals of Fig. 3 (f) carries out the robust watermarking image that extracts after the low-pass filtering treatment.

The robust watermarking image that the watermarked digital audio and video signals of Fig. 3 (g) extracts after resampling and handling.

The watermarked digital audio and video signals of Fig. 3 (h) carries out mp3 and compresses the robust watermarking image that extracts after the processing.

The watermarked digital audio and video signals of Fig. 3 (i) adds the robust watermarking image that extracts after the Gaussian noise of 20dB.

Digital audio and video signals time domain waveform figure after the watermarked digital audio and video signals of Fig. 4 (a) is distorted.

The time domain waveform figure of Fig. 4 (b) tampering location.

Embodiment

Below in conjunction with technical scheme and accompanying drawing, describe the specific embodiment of the present invention and embodiment in detail.

The embedding principle block diagram of the method for watermarking small wave threshold digital audio multiple mesh that separates based on blind source of the present invention as shown in Figure 1.Binary bitmap is carried out preliminary treatment, form by-1 and 1 sequence W ' that constitutes, by key I ₁Produce a chaos sequence, readjust the middle positions of elements of W ', form robust watermarking sequence W to be embedded according to this chaos sequence _rBy key I ₂Generate another chaos sequence as fragile watermark sequence W to be embedded _fThen, by means of the instantaneous mixed model in the separation theorem of blind source, with W _rAnd W _fThe approaching in the component that component and original audio signal third level small echo details component carry out that two-stage decomposes again of approaching that is embedded into original audio signal third level small echo in any order respectively.Wavelet coefficient after will handling through water mark inlaying carries out inverse transformation together in conjunction with not selected wavelet coefficient, can obtain to embed the audio signal of robust watermarking and fragile watermark.

The extraction of the method for watermarking small wave threshold digital audio multiple mesh that separates based on blind source of the present invention and distort and detect theory diagram as shown in Figure 2.Use the haar small echo to three grades of wavelet decomposition of audio signal S ' row to be detected, what obtain third level small echo approaches component cA3 ' and details component cD3 '.The location key information key1key1 that is kept when embedding with watermark selects the wavelet coefficient S that has embedded watermark _W1', as the two-way observation signal, utilize the FastICA algorithm in the independent component analysis to separate with the road key information key2 that keeps, obtain W _rAnd S _rEstimated value

With

Isolated two paths of signals is distinguished and judged by means of the quadravalence statistic, obtain

With sequence

In each element be that threshold value is carried out binary conversion treatment with zero, form by-1 and 1 sequence that constitutes, through reprocessing, the robust watermarking image that can obtain extracting

Three grades of small echo details components to audio signal S ' to be detected further carry out the two-stage wavelet decomposition, obtain it and approach component S _Wf1'.Check whether its length is consistent with the length of key information key3,, illustrate that audio-frequency information is modified if both length is inconsistent, no longer safe and reliable, do not carry out the extraction of fragile watermark; If both length is identical, then proceed the extraction of fragile watermark.With S _Wf1' with the road key information key3 that keeps as the two-way observation signal, utilize the FastICA algorithm in the independent component analysis to separate, obtain W _fAnd S _fEstimated value

With

By detecting

With Quadravalence statistics value, can judge audio signal and whether be distorted.With

As cD3 _A2' coefficient, other wavelet coefficient null representation, through after the wavelet inverse transformation, the time domain waveform figure of formation has reflected the situation of distorting for the treatment of detection signal.

Embodiment 1:

Original audio signal is chosen for one section voice signal, has considered adult male and two kinds of situations of women's childhood.When original audio signal was voice signal, the selection of parameter in the experiment was as follows: a _R1=0.75, a _R12=0.25, a _R21=0.99, a _R11=0.01; a _F11=0.97, a _F12=0.03, a _F21=0.95, a _F22=0.05; K=2048, th1=0.6, th2=20.Each section tested speech (being original audio signal) all is that monophony, sample frequency are that 8kHz, resolution are that 16 bits, length are 8.192s, and the time domain waveform figure of adult male voice signal is shown in Fig. 3 (a).Embed robust watermarking and fragile watermark audio signal afterwards shown in Fig. 3 (b).Comparison diagram 3 (a) and Fig. 3 (b) as can be seen, between the two without any difference; The test of people's audition also shows surplus in the of 10, and embedding two kinds of watermarks audio signal does not afterwards have perceptible distortion.

The robust binary bitmap is shown in Fig. 3 (c).Under the situation of not passing through any attack, the robust binary bitmap that extracts is shown in Fig. 3 (d).Comparison diagram 3 (c) and Fig. 3 (d) do not have any difference between the two as can be seen, and watermark information is more complete.I ₁During mistake (1% deviation), the binary bitmap that extracts is shown in Fig. 3 (e), and the algorithm among visible the present invention has good fail safe.The watermark bianry image that extracts after process low-pass filtering, resampling, mp3 compression and interpolation Gaussian noise are attacked is respectively shown in Fig. 3 (f)-3 (i).As can be seen, under the various attack situation, the robust binary bitmap that extracts is all more complete.

Three segment datas in the above-mentioned voice signal are revised, kept the total length of data constant, its time domain waveform figure carries out time domain waveform figure after the tampering location with the fragile watermark among the present invention shown in Fig. 4 (b) to it shown in Fig. 4 (a).As can be seen, this algorithm can carry out accurate localization to distorting.

Embodiment 2:

Original audio signal is chosen for one section music signal, has considered pop music, classical music and three kinds of situations of country music.When original audio signal was above-mentioned three kinds of music signals, the selection of parameter in the experiment was as follows: a _R11=0.90, a _R12=0.10, a _R21=0.99, a _R11=0.01; a _F11=0.97, a _F12=0.03, a _F21=0.95, a _F22=0.05 a _F22=0.05; K=2048, th1=0.6, th2=15.

Experimental result shows that for above several music signals, algorithm proposed by the invention can reach effect preferably equally.Especially attack resampling, the robustness when original audio signal is music signal will be far superior to voice signal.

Claims (1)

1. method for watermarking small wave threshold digital audio multiple mesh that separates based on blind source, comprise extraction, the fragile watermark of the preliminary treatment of Robust digital figure watermark and embedding, Robust digital figure watermark embedding, fragilely extract and distort detection; It is characterized in that: the preliminary treatment and the embedding of (1) Robust digital figure watermark: binary bitmap is carried out dimension-reduction treatment, the gray value that is about to its each pixel is end to end by row, formation is by 0 and 1 one-dimensional sequence that constitutes, again 1 in this sequence remained unchanged, 0 usefulness-1 is replaced, formation is by-1 and 1 sequence W that constitutes, by key I _tProduce one with the chaos sequence of W ' with length, readjust the middle positions of elements of W ' according to this chaos sequence, form robust watermarking sequence W to be embedded _fThen, by means of the instantaneous mixed model in the separation theorem of blind source, with W _fThe branch that approaches that is embedded in original audio signal third level small echo measures, and simultaneously, generate Robust Watermark Embedded Position key key1, and robust watermarking extracts required key key2;

(2) robust digitized map rubber watermark extracting: audio signal to be detected is carried out three grades of wavelet decomposition, and what obtain third level small echo approaches component cA3 ' and details component cD3 ', selects the wavelet coefficient S that has embedded watermark from cA3 ' with location key information key1 _Wy1', as the two-way observation signal, utilize a kind of blind source separation method that both are separated with key information key2, isolated two paths of signals is distinguished and judged by means of the quadravalence statistic, obtain robust watermarking sequence W _fEstimation

Will

In each element be that threshold value is carried out binary conversion treatment with zero, obtain by-1 and 1 sequence that constitutes, through being inverted unrest and inverse mapping, obtain, through rising after dimension handles the robust watermarking image that can obtain extracting by 0 and 1 binary sequence that constitutes

(3) embedding of fragile watermark: the details component cD3 to original audio signal third level small echo proceeds the two-stage wavelet decomposition, obtains it and approaches component cD3 _A2, be designated as S _f, by key I ₂Generate one and S _fWith the chaos sequence of length as fragile watermark sequence W to be embedded _fThen, by means of the instantaneous mixed model in the separation theorem of blind source, with W _fBe embedded in original audio signal third level small echo details component and carry out approaching in the component of two-stage decomposition again, simultaneously, generate fragile watermark and extract required key key3;

(4) fragile watermark extracts and distorts detection: three grades of small echo details component cD3 ' to audio signal to be detected further carry out the two-stage wavelet decomposition, obtain it and approach component cD3 _A2', be designated as S _Wf1', check cD3 _A2' length whether consistent with the length of key information key3, if both length is inconsistent, illustrate that audio-frequency information is modified, no longer safe and reliable, do not carry out the extraction of fragile watermark, identical as if both length, with S _Wf1' with the road key information key3 that keeps as the two-way observation signal, utilize a kind of blind source separation method that the two is separated, obtain W _fAnd S _fEstimated value

With

With W _fWith

Between coefficient correlation

Compare with prior preset threshold th1, if the former is greater than the latter, the content that audio signal to be detected then is described is safe, does not carry out any processing of distorting or resample, otherwise audio signal to be detected has been distorted or has been passed through to resample and handled; To handle two kinds of situations in order further distinguishing to distort and resample, need to judge by means of prior preset threshold th2; Isolated two paths of signals

With

In the value of road signal quadravalence statistic greater than th2, think that then audio signal is distorted, extract corresponding to this road signal of this quadravalence statistic

With

As cD3 _A2' coefficient,

Other wavelet coefficient null representation, through after the wavelet inverse transformation, among the time domain waveform figure that forms, the zone that amplitude is concentrated more a little louder the is corresponding position of being distorted, and the time domain waveform that reflects the signal that is used to replace original audio data, otherwise, think that this audio signal has been passed through resample to handle.

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