CN1889176A - Anti-DA/AD converting audio-frequency watermark processing method - Google Patents

Abstract

The invention is a method of the audio frequency watermark handling which is based on DWT, resisting DA/AD transposition; it belongs to the safety field of multi-media information. The invention has two processes, one is watermark insertion, the other is watermark monitor; the watermark is inserted in the low frequency sub-strip of minor wave modulus to resist the attack against overlaying noise; three section of minor wave modulus are a group to insert a bit watermark information to remove the effect of energy change, the multiunit insert many bits of watermark; designing the re-synchronization technology based on the synchronization code and interpolation operation to remove the effect of the stretch of time axis. The invention can not only resist the effect on watermark brought by DA/AD transposition in effect , but also have great solidity against common attack operation (such as MP3 compression , noise etc.). Besides to protect the audio frequency production to transmit in digital route, the invention can protect the audio frequency data crossed the DA/AD equipment, and be used to monitor advertisement of the music broadcasting station.

Description

A kind of audio-frequency watermark processing method of anti-DA/AD conversion

Technical field

The invention belongs to field of multimedia signal processing, be specifically related to a kind of audio-frequency watermark processing method of the anti-DA/AD conversion based on wavelet transform.

Background technology

In recent years, digital watermark technology had embodied its importance in many applications, and had obtained paying attention to widely.The research and the document of present most of data hiddens concentrate on image watermark.Along with being extensive use of of DAB, copy right piracy happens occasionally as using a hidden recorder by network download, DA/AD equipment etc.As a kind of effective means of protecting the audio frequency intellecture property, digital audio frequency watermark is being subjected to more and more people's attention.

Previous audio frequency watermark technology can be reduced two classes basically: Time-Domain algorithm and frequency domain algorithm.Time-Domain algorithm mainly contains LSB method, echo hiding (echo coding) etc.Frequency domain algorithm is hidden watermark by the frequency coefficient that changes sound signal, as discrete Fourier transform (DFT) (DFT), and the coefficient of discrete cosine transform (DCT) and wavelet transform (DWT).Frequency domain technique has robustness preferably usually, thereby the research of present audio frequency watermark mainly concentrates on frequency domain.The problem that may face when algorithm is primarily aimed on digital channel transmission in the past designs, and mainly considers the influence of MP3 compression, low-pass filtering etc., does not consider the problem that audio frequency watermark may be run in simulated environment basically.

Yet the extensive application demand wishes that audio frequency watermark can remain in the environment of simulation, as by analog channel transmission, prevent that the bootlegger from utilizing analog machine to transcribe etc.These application all relate to the DA/AD conversion, make the anti-D/A of audio frequency watermark and A/D be for conversion into a problem that urgency is to be solved.In the document of at present numerous relevant audio frequency watermark technology, all do not address this problem well.

Obviously, also lack the effective ways of guaranteeing that watermark exists under simulated environment at present.No matter be to consider, or, the audio frequency watermark technology that can resist the DA/AD conversion must be arranged all for for the music broadcast monitoring provides technological means for protection to the audio frequency copyright.Present audio frequency watermark technology can not satisfy this requirement.

Summary of the invention

In order to overcome the deficiencies in the prior art; the present invention proposes a kind of audio-frequency watermark processing method of anti-DA/AD conversion; compare with audio-frequency watermark processing method in the past; not only can resist the influence that is subjected to when audio frequency transmits under digital channel; as MP3 compression, superimposed noise and low-pass filtering etc.; and solved the problem of the indeterminable anti-DA/AD conversion of algorithm in the past, for the copyright of protecting voice data provides a kind of reliable means.

The concrete technical scheme of the inventive method is as follows: this method comprises watermark embedding and two processes of watermark detection;

The watermark embed process step is as follows: 1) audio frequency to be protected is divided into multiframe according to the watermark length that embeds, every frame audio frequency is carried out wavelet transform (DWT) and obtains the low frequency sub-band coefficient, from the low frequency wavelet coefficient of every frame audio frequency, select wavelet coefficient and be divided into many groups with key key1, every group by three the part form, be used to embed a bit information; 2) calculate respectively the wavelet coefficient of three different pieces in every group absolute value and; 3) by adjust three part wavelet coefficients in every group value come embed watermark information, every group embeds 1 bit; 4) repeating step 2) and 3) all embed up to watermark information; 5) amended DWT low frequency coefficient value is carried out the audio frequency that inverse transformation obtains having watermark;

Watermark detection process is as follows: identical during 1) with embedding, audio frequency is divided into multistage, carries out corresponding D WT conversion, will select some low frequency wavelet coefficients and be divided into many groups from every section audio with same key key1, and every component is three parts; 2) calculate every group of three part wavelet coefficients mould and, extract watermark bit by the relation between them relatively; 3) repeating step 2) step all extract up to watermark information.

The detailed step that described watermark embeds is: 1) synchronous code is the m sequence of certain-length, and the watermark information W that embed is expressed as binary sequence, and establishing watermark sequence is W={w _i, i=0,1 ... k-1, k are sequence length; 2) audio frequency that will protect is carried out the branch frame, carry out the low frequency wavelet coefficient that the DWT conversion obtains every frame audio frequency, utilize key key1 to obtain the coefficient of wanting embed watermark; 3) these coefficients are divided into a plurality of coefficient segments, three sections one group is divided into many groups; 4) L coefficient is a coefficient segments, is made up of 3L coefficient for one group, in every group of wavelet coefficient, calculates the absolute value sum of three sections wavelet coefficients respectively, is designated as E ₁, E ₂And E ₃, sort by size and be designated as E _Max, E _MedAnd E _Min, make A=E _Max-E _Med, B=E _Med-E _Min, establishing S is embedment strength, according to E ₁, E ₂And E ₃Size come dynamic value, make following agreement: when S≤A-B, represent that information bit is 1; Represent that information bit is 0 when S≤B-A, the embedding of watermark bit is to revise E by adjusting wavelet coefficient ₁, E ₂And E ₃Value realize; 5) repeating step 2), 3) and 4) all embed up to watermark information; 6) amended DWT coefficient is carried out contrary DWT conversion and generate watermarked audio;

The detailed step of described watermark detection is: 1) search is calculated the audio frequency length N between two synchronous codes in the synchronous code that embeds ₁, the audio frequency length N that is used for embed watermark information with it and before embedding between known two synchronous codes is compared, and obtains contraction-expansion factor, works as N=N ₁The time, be illustrated in not stretching on the time domain; 2) when having stretching, utilize interpolation algorithm to carry out linear extendible and recover, carry out watermark extracting again, as not stretching, then directly audio frequency is carried out the branch frame and extract watermark information; 3) use key key1 identical when embedding that the DWT low frequency coefficient in each frame is selected, divide into groups to calculate watermark bit; 4) watermark bit of extracting is expressed as final watermarking information again.

Described watermark detection step 2) the flexible concrete grammar that recovers of neutral line is as follows:

Suppose F '=f ' (0), f ' (1) ... f ' (L '-1) } be the watermarked audio after handling through D/A and A/D, be N by extracting the audio frequency length that synchronizing signal calculates between two synchronizing signals ₂', N ₂For the known audio frequency length of watermarked audio F between preceding two synchronizing signals of conversion, work as N ₂' ≠ N ₂Shi Caiyong formula (11) carries out linear extendible and recovers, and is equivalent to the process of an interpolation,

F "={ f " (0) wherein, f " (1) ... f " (L-1) be the watermarked audio after linear extendible recovers, the i of f " (i) (j) be respectively F with f ' " and F ' individual with j sample, 0≤i≤L-1,0≤j≤L '-1,

Be bracket function, α=(N ₂'/N ₂)=(L '-1)/(L-1) be the linear extendible factor, L ' and L are respectively audio frequency F ' and F " length.

The present invention not only can effectively resist the influence that the watermark of DA/AD transfer pair brings, and for some common attack operation (as MP3 compression, noise etc.) extraordinary robustness is arranged also.Except can protecting the transmission of audio production on digital channel, the present invention can protect those voice datas that passes through DA/AD equipment, also can be used for the monitoring of music radio station advertisement.

Description of drawings

Fig. 1 is the FB(flow block) that watermark embeds;

Fig. 2 is the FB(flow block) of watermark detection;

Fig. 3 is three sections adjacent low frequency wavelet coefficient segmentation synoptic diagram;

Fig. 4 is the noise synoptic diagram of audio frequency in the DA/AD conversion;

Fig. 5 is the audio volume control figure that is used to test;

Fig. 6 is the oscillogram of audio frequency before and after embed watermark;

Fig. 7 is audio frequency oscillogram after the DA/AD conversion.

Embodiment

Below in conjunction with accompanying drawing the inventive method is described further.

This comprises watermark embedding and two processes of watermark detection the audio-frequency watermark processing method of a kind of anti-DA/AD conversion of the present invention.

1. watermark embeds

The telescopiny of watermark at first with a segment length audio parsing, is hidden a synchronizing signal and part (or all) watermark data as shown in Figure 1 in every section audio.Specific practice is earlier every section audio to be made wavelet decomposition, and synchronizing signal and watermark is converted to { 1, the 1} sequence then will { 1, the sequence of 1} be embedded in the low frequency coefficient in DWT territory.The mode that adopts self-adaptation to regulate embedment strength when watermark embeds obtains the maximum that satisfies under the audio quality prerequisite.Watermark embeds audio frequency is directly calculated in the back in the DWT territory SNR value, if the SNR value meets the demands, then carry out the audio frequency that wavelet reconstruction has obtained being embedded with watermark, otherwise adjust embedment strength according to certain rule (following table 1), SNR value after embedding reaches the requirement of predesignating, and carries out the audio frequency that wavelet reconstruction obtains being embedded with watermark again.

Table 1

The embedment strength factor	SNR behind the audio frequency embed watermark
		D increases, S LAnd S URemain unchanged	The SNR value reduces.
S LIncrease, d and S URemain unchanged	The SNR value reduces, S LWhen increasing to a certain degree, SNR no longer changes.
		S UIncrease, d and S LRemain unchanged	The SNR value reduces, S UWhen increasing to a certain degree, SNR no longer changes.

Concrete embedding grammar is described below:

M sequence (synchronous code) and watermark all are converted to the sequence of " 1 " and " 1 ".And tectonic sequence syn (i) and wmk (i).Every frame embeds information { w (i) }, and { { 1, the length of 1}} is the length sum of m sequence syn (i) and watermark information wmk (i) to w (i) ∈.The m sequence is put into the front portion of { w (i) }, and watermark information is put into the rear portion of { w (i) }.The structure of hiding data is as shown in table 2 below:

Table 2

……

Synchronizing signal

Watermark information

Synchronizing signal

Watermark information

……

In table 2, one segment length's sound signal is carried out segmentation by the mode of table 3 according to the length of synchronizing signal and watermark information:

Table 3

……

Section length N1

Section length N2

Section length N1

Section length N2

……

After the voice data segmentation, to data segment N ₁And N ₂Make the wavelet decomposition of k layer, will obtain N respectively ₁/ 2 ^kAnd N ₂/ 2 ^kIndividual low frequency wavelet coefficient is then at N ₁/ 2 ^kEmbed synchronizing signal in the individual low frequency coefficient, at N ₂/ 2 ^kEmbed watermark information in the individual low frequency coefficient, thus the embedding of a frame information { w (i) } finished.

The change of energy discharge amplitude can take place in sound signal in D/A and A/D process, had a strong impact on the verification and measurement ratio based on the embedding grammar of audio frequency signal amplitude absolute magnitude.So the energy relationship between the adjacent low frequency wavelet coefficient comes embed watermark to this paper embedding grammar based on three sections in employing, thereby avoided and to have changed the problem of bringing by discharge amplitude.Because embedding is to carry out at frequency domain, has stronger robustness.

In the table 3, the length N of segmentation ₁And N ₂Respectively by the length of synchronizing signal and watermark information and the wavelet decomposition number of plies and embedment strength decision, promptly

N ₁=3L * 2 ^k* (synchronous code length) (1)

N ₂=3L * 2 ^k* (watermark information length) (2)

Wherein, k is the wavelet decomposition number of plies, and L is the length of one section low frequency wavelet coefficient, and its selection requires relevant with embedding bandwidth, SNR and anti-attack.Suppose to have 3L adjacent low frequency wavelet coefficient c (i) | i=0 ... 3L-1}, it is equally divided into 3 sections, every segment length L, as shown in Figure 3.

The ENERGY E that three sections low frequency wavelet coefficients are then arranged ₁, E ₂And E ₃Be defined as follows:

$E_1=\underset{i=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\left|c\left(i\right)\right|,$ $E_2=\underset{i=\mathrm{<figure-callout\; id="2L"\; label="L"\; filenames="A20061003649900153.png"\; state="\{\{state\}\}">L</figure-callout>}}{\overset{2L-1}{\mathrm{\&Sigma;}}}\left|c\left(i\right)\right|,$ $E_3=\underset{i=2\mathrm{<figure-callout\; id="3L"\; label="L"\; filenames="A20061003649900153.png"\; state="\{\{state\}\}">L</figure-callout>}}{\overset{3L-1}{\mathrm{\&Sigma;}}}\left|c\left(i\right)\right|$

Order: $\left\{\begin{array}{c}A=E_{\max }-E_{\mathrm{med}}\\ B=E_{\mathrm{med}}-E_{\min }\end{array}---\left(3\right)\right.$

Wherein, E _Max=max{E ₁, E ₂, E ₃, E _Med=midian{E ₁, E ₂, E ₃, E _Min=min{E ₁, E ₂, E ₃.

Definition: $S=\left\{\begin{array}{ccc}{P}_L& \mathrm{if}& (d\&CenterDot;\underset{i=0}{\overset{3L-1}{\mathrm{\&Sigma;}}}|c\left(i\right)\left|\right)/3<P_L\\ P_U& \mathrm{if}& (d\&CenterDot;\underset{i=0}{\overset{3L-1}{\mathrm{\&Sigma;}}}|c\left(i\right)\left|\right)/3>P_U\\ (d\&CenterDot;\underset{i=0}{\overset{3L-1}{\mathrm{\&Sigma;}}}|c\left(i\right)\left|\right)/3& & \mathrm{others}\end{array}\right.---\left(4\right)$

1), then make A and B satisfy if the information w (i) that embeds is " 1 ":

A-B≥S (5)

As not satisfying the relation of formula (5), then adjust E simultaneously _Max, E _MidAnd E _MinThree's size.

2) if the information w that embeds (i} be " 1 ", then makes A and B satisfied:

B-A≥S (6)

In like manner, if the relation of formula (6) is false, then adjust E simultaneously _Max, E _MidAnd E _MinThree's size.

D in the formula (4) is that embedment strength is adjusted the factor, and it has determined extent between A and the B, owing in D/A and A/D conversion process certain waveform distortion is arranged, therefore can adjust d according to the requirement of anti-attack ability, to satisfy actual needs.Simultaneously, d also is the key factor that influences audio signal quality behind the embed watermark, should get big value under the prerequisite that guarantees watermarked audio imperceptible (certain SNR value) as far as possible.P _UAnd P _LBe respectively the bound of embedment strength, determined the size of watermark anti-attack ability.Noise effect in D/A and the A/D conversion process is very big, adopts lower limit P _LGuarantee the anti-attack ability of watermark.P _UBe the embedment strength upper limit, restriction can improve the SNR value of watermarked audio because of embedment strength s influence to watermarked audio when excessive.P _UAnd P _LSelection relevant with intensity, the wavelet decomposition number of plies of audio frequency with section length L.The large and small more wavelength-division of audio frequency intensity separates that the number of plies is many more, section length L is big more, and the value of bound is also big more.Embedment strength factor d, lower limit factor S _LWith upper limit factor S _UInfluence to audio frequency SNR value is as shown in table 1.

2. watermark detection

In the process of D/A and A/D, may be subjected to flexible influence on time shaft according to audio frequency watermark, when using synchronous code, propose the method for detecting watermarks that recovers based on linear extendible.The watermark detection flow process is as shown in Figure 2:

At first sound signal to be detected being carried out linear extendible when extracting watermark recovers, corresponding wavelet decomposition is made in segmentation again, from low frequency coefficient, search for synchronizing signal, find the reference position of embed watermark information, from the DWT low frequency coefficient of sample subsequently, extract watermark then.Linear extendible recovers to know the length of former audio frequency, so that the flexible factor of recovering of decision.Feasible way is by searching two synchronous codes, and known original audio length is calculated contraction-expansion factor between two synchronous codes when embedding according to the audio frequency length between them and watermark, and then carries out linear extendible and recover.Therefore this scheme does not need original audio-frequency information in the process of watermark detection, is a kind of blind Audio Watermarking Algorithm.

Recover by linear extendible, eliminated audio frequency flexible influence that is brought on time shaft.And the introducing of synchronizing signal and reorientation search can be located the starting point that each frame embeds information, and then extract watermark.

1) linear extendible recovers

Suppose F '=f ' (0), f ' (1) ... f ' (L '-1) } be the watermarked audio after handling through D/A and A/D, be N by extracting the audio frequency length that synchronizing signal calculates between two synchronizing signals ₂', N ₂For the known audio frequency length of watermarked audio F between preceding two synchronizing signals of conversion, work as N ₂' ≠ N ₂Shi Caiyong formula (11) carries out linear extendible and recovers, and is equivalent to the process of an interpolation.

F "={ f " (0) wherein, f " (1) ... f " is (L-1) } be the watermarked audio after linear extendible recovers, the i of f " (i) (j) be respectively F with f ' " and F ' individual with j sample, 0≤i≤L-1,0≤j≤L '-1,

Be bracket function, α=(N ₂'/N ₂)=(L '-1)/(L-1) be the linear extendible factor, L ' and L are respectively audio frequency F ' and F " length.

2) detection algorithm

Suppose to have determined the starting point of audio frequency to be detected, the chopping rule in the time of then will be according to embed watermark is the voice data segmentation, and does the wavelet decomposition of the corresponding number of plies, obtains low frequency wavelet coefficient f ' (i), calculates corresponding E according to same length 3L ₁', E ₂' and E ₃', the process that similar watermark embeds further obtains E _Max', E _Med' and E _Min', calculate then:

$\left\{\begin{array}{c}{A}^{\&prime;}={E^{\&prime;}}_{\max }-{E^{\&prime;}}_{\mathrm{med}}\\ B^{\&prime;}={E^{\&prime;}}_{\mathrm{med}}-{E^{\&prime;}}_{\min }\end{array}---\left(12\right)\right.$

Then have:

$w^{\&prime;}\left(i\right)=\left\{\begin{array}{ccc}1& \mathrm{if}& A^{\&prime;}-B^{\&prime;}\&GreaterEqual;0\\ -1& \mathrm{if}& A^{\&prime;}-B^{\&prime;}<0\end{array}---\left(13\right)\right.$

Following table 4 has shown the situation of audio frequency (5 kinds of different sound cards) sample generation conversion in the DA/AD conversion.The situation of this variation and the performance of sound card, the sampling rate when playing and recording are relevant.

Table 4

Following table 5 has shown the error condition of audio frequency watermark under Gaussian noise, MP3 compression, low-pass filtering, weightization and resampling.As can be seen, processing is very sane to the watermarking algorithm among the present invention to normal signal.

Table 5

Attack type	BER(％)	Attack type	BER(％)
				Do not have and attack	0	Gaussian noise (8dB)	0
MP3(32kbps)	0	MP3(128kbps)	0
				Weightization (16-8-16bit)	0	Resample (44.1-8-44.1kHz)	0
LPF (cutoff frequency is 9kHz)	0	Amplitude stretch (10%～150%)	0

Among Fig. 4,, utilize a cable to link the Line in interface of sound card then, again by the recording software recording audio by the quiet loudspeaker output of player plays by sound card.Because what play is quiet, reflected noise situations in the DA/AD conversion so record waveform.

Among Fig. 5, the original audio that is used to test is that a first quantified precision is 16, sample frequency is 44100Hz, monophony, length are about 56 seconds whistling music.Be expressed as Original.wav.

Among Fig. 6, to get one-period be 31 m sequence to synchronizing signal when embedding information, and threshold value T is taken as 23, and watermark is the scale-of-two random series of one 32 bit long.Select the db2 wavelet basis, the decomposition number of plies of small echo is 7, and the length of L gets 8.Audio representation after the embedding information is Water.wav.Before go into the back SNR be more than the 20dB, acoustically can not distinguish the difference of original audio and watermarked audio.

Among Fig. 7,, utilize a cable to link the Line in interface of sound card then, again by the recording software recording audio by the loudspeaker output of player plays Water.wav by sound card.Record waveform and reflected the situation of watermarked audio after the DA/AD conversion.As can be seen, after the DA/AD conversion, the energy integral body of audio frequency has changed.

Claims (4)

1, a kind of audio-frequency watermark processing method of anti-DA/AD conversion is characterized in that this method comprises watermark embedding and two processes of watermark detection;

The watermark embed process step is as follows: 1) audio frequency to be protected is divided into multiframe according to the watermark length that embeds, every frame audio frequency is carried out wavelet transform (DWT) and obtains the low frequency sub-band coefficient, from the low frequency wavelet coefficient of every frame audio frequency, select wavelet coefficient and be divided into many groups with key key1, every group by three the part form, be used to embed a bit information; 2) calculate respectively the wavelet coefficient of three different pieces in every group absolute value and; 3) by adjust three part wavelet coefficients in every group value come embed watermark information, every group embeds 1 bit; 4) repeating step 2) and 3) all embed up to watermark information; 5) amended DWT low frequency coefficient value is carried out the audio frequency that inverse transformation obtains having watermark;

Watermark detection process is as follows: identical during 1) with embedding, audio frequency is divided into multistage, carries out corresponding D WT conversion, will select some low frequency wavelet coefficients and be divided into many groups from every section audio with same key key1, and every component is three parts; 2) calculate every group of three part wavelet coefficients mould and, extract watermark bit by the relation between them relatively; 3) repeating step 2) step all extract up to watermark information.

2, the audio-frequency watermark processing method of a kind of anti-DA/AD conversion according to claim 1, it is characterized in that the detailed step that described watermark embeds is: 1) synchronous code is the m sequence of certain-length, the watermark information W that will embed is expressed as binary sequence, and establishing watermark sequence is W={w _i, i=0,1 ... k-1, k are sequence length; 2) audio frequency that will protect is carried out the branch frame, carry out the low frequency wavelet coefficient that the DWT conversion obtains every frame audio frequency, utilize key key1 to obtain the coefficient of wanting embed watermark; 3) these coefficients are divided into a plurality of coefficient segments, three sections one group is divided into many groups; 4) L coefficient is a coefficient segments, is made up of 3L coefficient for one group, in every group of wavelet coefficient, calculates the absolute value sum of three sections wavelet coefficients respectively, is designated as E ₁, E ₂And E ₃, sort by size and be designated as E _Max, E _MedAnd E _Min, make A=E _Max-E _Med, B=E _Med-E _Min, establishing S is embedment strength, according to E ₁, E ₂And E ₃Size come dynamic value, make following agreement: when S≤A-B, represent that information bit is 1; Represent that information bit is 0 when S≤B-A, the embedding of watermark bit is to revise E by adjusting wavelet coefficient ₁, E ₂And E ₃Value realize; 5) repeating step 2), 3) and 4) all embed up to watermark information; 6) amended DWT coefficient is carried out contrary DWT conversion and generate watermarked audio;

3, the audio-frequency watermark processing method of a kind of anti-DA/AD conversion according to claim 1 and 2 is characterized in that the detailed step of described watermark detection is: 1) search is calculated the audio frequency length N between two synchronous codes in the synchronous code that embeds ₁, the audio frequency length N that is used for embed watermark information with it and before embedding between known two synchronous codes is compared, and obtains contraction-expansion factor, works as N=N ₁The time, be illustrated in not stretching on the time domain; 2) when having stretching, utilize interpolation algorithm to carry out linear extendible and recover, carry out watermark extracting again, as not stretching, then directly audio frequency is carried out the branch frame and extract watermark information; 3) use key key1 identical when embedding that the DWT low frequency coefficient in each frame is selected, divide into groups to calculate watermark bit; 4) watermark bit of extracting is expressed as final watermarking information again.

4, the audio frequency watermark technology of a kind of anti-DA/AD conversion according to claim 3 is characterized in that described watermark detection step 2) the flexible concrete grammar that recovers of neutral line is as follows:

Suppose F '=f ' (0), f ' (1) ... f ' (L '-1) } for through the watermarked audio after D/A and the A/D processing, be N by the audio frequency length of extracting between two synchronizing signals of synchronizing signal calculating ₂', N ₂For the known audio frequency length of watermarked audio F between preceding two synchronizing signals of conversion, work as N ₂' ≠ N ₂Shi Caiyong formula (11) carries out linear extendible and recovers, and is equivalent to the process of an interpolation,

F "={ f " (0) wherein, f " (1) ... f " (L-1) be the watermarked audio after linear extendible recovers, the i of f " (i) (j) be respectively F with f ' " and F ' individual with j sample, 0≤i≤L-1,0≤j≤L '-1, β=α i- α i  ∈ [0,1],   is a bracket function, α=(N ₂'/N ₂)=(L '-1)/(L-1) be the linear extendible factor, L ' and L are respectively audio frequency F ' and F " length.

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