CN101944362A - Integer wavelet transform-based audio lossless compression encoding and decoding method - Google Patents

Abstract

The invention discloses an audio lossless compression encoding and decoding method, which belongs to the field of information source encoding and decoding. This method adaptively divides the signal into frames according to the relevant conditions of the frames before and after the signal. The framed signal is a combination of signals with similar signal characteristics, so that the encoder can obtain better compression efficiency, which is the following integer wavelet Transform and linear predictive coding bring benefits. For lossless compression coding, the signal should be completely reconfigurable, so the integer lifting wavelet transform is used to ensure the completely reconfigurable characteristics of the signal. Compared with the prior art, after the present invention introduces the adaptive framing module based on correlation and the de-correlation module based on integer lifting wavelet, the redundant information in the original signal can be better de-correlated, and the generated compressed The redundant information contained in the data is less, so the present invention can obtain a larger compression ratio improvement with a small calculation complexity cost.

Description

A Lossless Audio Compression Encoding and Decoding Method Based on Shaping Wavelet Transform

technical field

The invention belongs to the field of information source encoding and decoding, and in particular relates to an audio lossless compression encoding and decoding method.

Background technique

With the advent of the digital age, the digitalization of audio signals has brought a lot of convenience to people while generating massive audio data, which has brought great challenges to the storage and transmission of audio signals, and has become an obstacle that hinders people from obtaining and using multimedia. One of the information bottlenecks. In order to solve this problem, it is necessary to compress the audio data, and store and transmit the data in a compression coded manner. Facts have proved that it is necessary and feasible to compress multimedia data, because there is strong redundant information in multimedia data information such as sound and image, that is, there is a strong correlation between data, which can be removed by removing redundant information ( That is to remove the correlation between data), retain useful audio information to achieve compression. Therefore, it is an inevitable choice to research and develop efficient audio coding methods to store and transmit audio information in a compressed form. Moreover, with the improvement of people's requirements for audio quality, how to compress audio data with the largest possible compression ratio under the condition of retaining all audio information, so as to provide people with truly transparent sound quality, has become the main problem faced by current audio compression coding. topic.

As early as the 1970s, broadcasting departments in the United Kingdom and Japan began to study digital audio lossy compression coding. After 40 years of development, many excellent coding standards have emerged in the current lossy audio compression coding standards. Among them are representative There are MP3, AAC, WMA, etc. These encoding formats can achieve good subjective sound quality and high compression ratio in many cases, but when they encounter music with a large frequency dynamic range, such as large-scale symphonies, etc., these The sound quality performance after lossy audio encoding is unsatisfactory. In addition, in the field of audio editing, performing secondary encoding on lossy compression-encoded audio data (that is, conversion between two lossy encoding formats) will lose more information, thereby introducing greater distortion. In order to solve the above-mentioned problems and meet some requirements for sound quality, it is necessary to use lossless compression coding.

Compared with lossy compression coding, the research and application of lossless compression coding for audio signals are rare. The reason why lossless compression has not received enough attention is that its compression ratio is difficult to exceed 3:1, while lossy algorithms can achieve a compression ratio of 12:1 or even higher. But for the lossy compression algorithm, the higher the compression ratio, the worse the final audio quality will be. Once the lowest possible data rate is determined, the lossy compression algorithm is the only choice. However, music lovers want to download high-fidelity stereo audio signals from the Internet in order to obtain the best music effects. Therefore, online music promotion will provide audio signals with higher compression ratios for different consumers to browse and choose. Music lovers of audio quality want a lossless compressed copy of the original audio signal - a backup without any signal loss due to differences in compression algorithms. In addition to being available for online audio signal download, lossless audio compression coding can also be applied to archiving, mixing, studio, program production, etc. of high-fidelity audio data in professional environments. In this case, lossless compression avoids the signal loss caused by multiple edits that would otherwise occur with lossy compression encoding.

From the point of view of information theory, the audio signal is regarded as a source, and the data describing the source is the sum of the amount of information (information entropy) and the amount of information redundancy. Almost all lossless audio compression is based on a similar idea, first removing redundancy from the signal, only the amount of redundancy in the data is removed, without reducing the amount of information in the source. Then encode with an efficient data encoding scheme. There are many kinds of redundancies in the audio signal, mainly including the non-uniformity of signal amplitude distribution, the correlation between adjacent samples, and the correlation between periods. So the main idea of the lossless compression coding algorithm is how to effectively remove the redundancy in the audio signal. At present, the formats of well-known audio lossless coding algorithms include FLAC (Free Lossless Audio Codec), WavPack, TAK (Tom's Audio Kompressor), APE (Monkey's Audio), OFR (OptimFROG), ALAC (Apple Lossless Audio Codec) , WMAL (Windows Media Audio Lossless), Shorten, LA (Lossless Audio), TTA (Ture Audio), LPAC (Lossless Predictive Audio Coder), RAL (Real Audio Lossless), MPEG-ALS, etc. These algorithms mainly use two methods for de-correlation and further lossless compression coding: one is based on time domain linear predictive coding (LPC) technology, and the other is based on transform domain technology such as IntMDCT (Integer Modified Discrete Cosnie Transform , integer modified discrete cosine transform). The goal of lossless compression is to remove redundancy in the data and perfectly reconstruct the original audio signal. Linear predictive coding can further reduce redundancy, especially for those signals with stationary characteristics. Generally speaking, a smooth sound signal has more information redundancy, while a dissonant (noise-like) signal has less information redundancy. The size of a specific sample value is related to its neighboring sample values. Generally speaking, the current sample value is closer to the previous sample value. This is especially true for low frequency signals.

At present, the main idea of the mainstream linear predictive coding method is reflected in the decorrelation part, so that the data handed over to the entropy coding module is more suitable for compression using the entropy coding method, so that the entropy coding can have better compression performance for the data to be coded . The basic principle of the linear predictive coder is to use the correlation of the sound signal to predict the current sample value x[n] with the past sample value x[n-1], x[n-2]..., and use the past sample value x[n-2]... The more samples, the higher the prediction accuracy. Then subtract the current sample value from the predicted value and take the difference (prediction error) for encoding. Since the dynamic range of the prediction error is much smaller than that of the original signal, even if the quantization level used in the quantization of the original signal is still used at this time, the code bits can be reduced for encoding, thereby realizing bit rate compression. For example, for a sound with gentle amplitude fluctuations, the prediction error will vary between zero and a small value, the mean value of e[n] will be much smaller than x[n], and the prediction error e[n] between adjacent samples is basically are uncorrelated and have a flat spectrum. Therefore, fewer data bits are needed to represent its actual value. The commonly used entropy coding is RICE code, which has a simple coding and decoding process and does not need to know the prior distribution of the signal when coding, so it is widely used in audio lossless compression. After RICE encoding, the data that can obtain a larger compression rate generally has the following characteristics: First, the amplitude is small, because the coding process needs to be quantized at the end, and the small amplitude means that it can be compressed with a small number of bits. The second is that the correlation between the data is small, and the third is that the data distribution is as close to the geometric distribution as possible. When linear predictive coding is used for decorrelation, the redundancy of the original audio signal is not completely removed, that is, the decorrelation is not complete. That is, the prediction error data input to the entropy encoding module still has redundant information, and there is a certain correlation between adjacent sample values of the error signal, which can be further processed.

Contents of the invention

The purpose of the present invention is to provide a method for audio lossless compression encoding and decoding, which uses a correlation coefficient-based framing strategy to adaptively divide the signal into frames according to the correlation of the frames before and after the signal, so that the signals in one frame have a strong correlation The one-frame signal after framing is a combination of signals with similar signal characteristics, so that the encoder can obtain better compression efficiency and bring benefits to the subsequent integer wavelet transform and linear predictive coding. In order to make the residual amplitude as small as possible, linear prediction is required to be as accurate as possible, and linear predictive coding has good predictive ability for highly correlated signals, so it is considered to use wavelet transform to process the signal in bands, because within a narrow band The signal correlation of the signal will be better than that of the full-band signal, so the wavelet transform of the signal is more conducive to removing the correlation of the sample points; for lossless compression coding, the signal should be completely reconstructed, so it is necessary to Integer lifting wavelet transform is used to ensure the fully reconfigurable characteristics of the signal. After we introduce the correlation-based adaptive framing module and the integer lifting wavelet-based de-correlation module, the redundant information in the original signal can be better de-correlated, and the redundant information contained in the generated compressed data Fewer, so we can use a small computational complexity cost in exchange for a large compression ratio improvement.

The present invention includes correlation-based self-adaptive framing technology, lift-based integer wavelet transform de-correlation technology and other related technologies involved in encoding and decoding. It can provide a higher compression ratio than the audio lossless encoding and decoding system using linear prediction technology to decorrelate alone.

The audio lossless codec system according to the inventive method can be divided into two parts of encoder subsystem and decoder subsystem:

The encoder subsystem includes:

Framing module: used for adaptive framing of the input audio signal;

Integer wavelet transform module: used to process a section of audio signal after framing;

Linear predictive coding module: used to linearly predict the signal in each subband to remove the correlation between adjacent samples;

Entropy coding module: used for lossless source coding of the residual signal output by the linear predictive coding module

Bit stream forming module: used to form the entropy encoded stream, frame length information, wavelet classification information, LPC parameters and codebook information formed in the above modules into a bit stream in a certain format and write it into a file;

The decoder subsystem includes:

Bit stream separation module: used to separate the bit stream in the compressed audio file according to the specified format, and generate different data such as entropy encoded stream, frame length information, wavelet classification information, LPC parameters, codebook information, etc.;

Entropy decoding module: used to completely regenerate the residual signal by decoding the entropy encoded stream

LPC reconstruction module: used to reconstruct the LPC parameters and residual signal in the side information into sub-band signals after wavelet transform.

Integer Lifting Wavelet Reconstruction Module: Used to resynthesize the sub-band signal after wavelet decomposition into a complete audio signal frame.

Merge frame module: Merge each frame of reconstructed audio signal into an audio PCM file, write it into the file header of the WAVE file, and generate the decompressed WAVE file.

The specific implementation of the audio signal lossless encoding/decoding method according to the present invention is as follows:

The lossless encoding process of the audio signal is that the audio file is first divided into several frames according to the framing strategy, and the framing information (that is, the frame length information) is included in the side information transmission; each frame is processed separately, that is, the approximate signal and the detail signal are first obtained through the wavelet transform, and the wavelet The decomposition series (that is, the wavelet classification information) is obtained according to the adaptive rules, and the decomposition series is also included in the side information; the approximate signal and the detail signal are obtained through the linear prediction module. Residual signal and LPC parameters, the residual signal obtained in the linear prediction module The entropy coded stream is obtained through entropy coding, and the LPC parameters and the codebook information of the entropy code are included in the side information. Finally, each code stream (ie, the side information and the entropy coded stream) is multiplexed to form the final compressed code stream.

The lossless decoding process of the audio signal is actually the reverse process of the encoding process. By first decoding the side information, the entropy codebook, LPC parameters, classification information and frame length information are separated from the side information. The entropy coding module is based on the codebook The information is entropy decoded, and the residual signal after LPC prediction is obtained from the entropy encoded stream. The LPC reconstruction module uses the LPC parameters to obtain the approximate signal and detail signal of the wavelet decomposition from the residual signal. According to the wavelet classification information, the approximate signal and the detail signal are reconstructed to obtain the signal of each frame, and finally the frames are connected sequentially according to the frame information to obtain the original audio file without loss.

The audio lossless coder/decoder system according to the method of the present invention includes two parts: a coder subsystem and a decoder subsystem. The main key technologies used in the whole system are correlation-based adaptive framing technology, integer lifting wavelet transform technology, adaptive linear predictive coding technology, and Rice code entropy coding technology for geometrically distributed data. The following will introduce each technical content:

1. Correlation-based adaptive framing technology

The word frame comes from image, which means to divide a continuous moving image into pictures. Comics are a good example. Borrowing "frame" in digital audio means that the analog signal is converted into a digital signal, and the digital signal is divided into many small segments, which are called 1 frame. Since there are quite a lot of abrupt changes in the audio signal, if a fixed frame length is used for framing, the correlation between the obtained signals in each frame will be greatly affected, thereby reducing the compression rate.

According to the correlation coefficients of adjacent frames, the present invention combines signals with high correlation into one frame, so that the compactness of wavelet transformation and linear prediction can be improved, and higher compression efficiency can be obtained. First, calculate the correlation coefficient between the current frame and the previous frame with the minimum frame length as the unit. If the coefficient is less than the threshold, mark the frame and the previous frame as irrelevant frames and form a single frame. If the coefficient is greater than the threshold, it is considered The current frame is related to the previous frame, and the adjacent related frames are merged sequentially, but the maximum frame length does not exceed the set maximum frame length allowable value. When the length of the merged frame exceeds the set maximum frame length, restart a frame . By adopting the above framing strategy, signals with consistent characteristics can be processed within one frame.

2. Integer wavelet transform technology

Integer wavelet transform is a wavelet transform that maps integers to integers, that is, the input signal is an integer, and the transformed wavelet coefficients are also integers, and the original signal can be accurately restored by the inverse transform. The coefficients generated after traditional wavelet transform are floating-point numbers, which not only requires a lot of calculation, but also cannot achieve lossless data compression. The wavelet transform is calculated by using the lifting scheme, and the wavelet transform from integer to integer can be realized by adding quantization operation in the lifting process. Integer wavelet transform has many applications in the field of image compression, and can realize low-complexity embedded coding from lossy to lossless, but it has not been well applied in lossless compression of audio signals.

The traditional transform method, no matter it is fast Fourier transform or wavelet transform, the input signal is an integer, and the transformed coefficient is a floating-point number. There are rounding errors in the computer processing, and the lossless data compression cannot be realized. Consider adding a quantization operation in the lifting step. If the input vector x is an integer, the output y is also an integer, and x can be accurately recovered from y. It should be noted that the role of quantization here is different from that in data compression. , the quantization does not bring information loss, but only for integer output. Integer wavelet transform is a kind of nonlinear transformation because it includes quantization operation, which makes the analysis of integer wavelet transform more complicated. In practical applications, if the form of quantization operation is properly selected, the integer wavelet transform can be regarded as a linear transformation to simplify the analysis.

From the perspective of multi-resolution analysis or band-pass filter, wavelet decomposition is not limited to the above-mentioned one-level decomposition, and wavelet decomposition can be continued on the approximate signal after one-level decomposition to further remove its correlation, but due to Different signals have different frequency distributions, and the use of different decomposition levels will have an impact on the compression results. The method of the present invention adaptively selects the levels according to the compression effect after signal decomposition, so that the compression results can be optimized, and the The best decomposition level information is recorded in the side information.

3. Adaptive linear predictive coding technology

The higher the prediction accuracy of the lossless audio encoder, the higher the encoding efficiency. Most algorithms remove redundancy through some modified linear predictor, which is applied to each frame of data, producing a sequence of prediction errors. The parameters of the predictor represent the redundancy removed from the signal, and the parameters of the lossless coded predictor together with the prediction error represent the signal for each frame.

The basic principle of the linear predictor is to use the correlation of the sound signal to predict the current sample value x[n] with the past sample values x[n-1], x[n-2],...etc. , the more past samples are used, the higher the prediction accuracy will be. Then subtract the current sample value from the predicted value and take the difference (prediction error) for encoding. Since the dynamic range of the prediction error is much smaller than that of the original signal, even if the quantization level used in the quantization of the original signal is still used at this time, the code bits can be reduced for encoding, thereby realizing bit rate compression. This method is especially effective for those sound signals with stationary characteristics. For example, for sounds with flat amplitude fluctuations, the prediction error will vary from zero to a very small value. If the predictor works well, the prediction errors e[n] are uncorrelated and have a flat spectrum. Likewise, e[n] will have a smaller mean than x[n], requiring fewer data bits to represent its actual value.

Linear predictors are widely used in speech and audio signal processing. In most cases, using FIR filters, the coefficients of the prediction filter A(z) are determined to minimize the mean squared prediction error. If the quantizer is not considered, the FIR prediction coefficients can be obtained by solving a set of linear equations. If the FIR filter is used in lossless audio compression, the coefficients can be obtained through certain steps and then quantized, and the same coefficients can be used to reconstruct x[n] from e[n] at the decoding end. Since the original signal must be completely lossless reconstructed, the prediction coefficients (that is, the LPC parameters) must be quantized and encoded as part of the lossless audio encoding. Usually, in order for the predictor to adapt to changes in the signal, a new set of prediction coefficients must be determined for each frame after framing.

4. Rice code entropy coding technology for geometrically distributed data

The theoretical basis of data compression technology is information theory. The main problems solved by source coding theory in information theory: (1) The theoretical limit of data compression (2) The basic way of data compression. According to the principle of information theory, the best data compression coding method can be found, and the theoretical limit of data compression is information entropy. Information entropy is the average amount of information (a measure of uncertainty) of a source. If it is required that the amount of information is not lost during the encoding process, that is, information entropy is required to be preserved. This kind of information-preserving encoding is called entropy encoding. It is carried out according to the distribution characteristics of the probability of occurrence of the message, and in this process, the redundancy in the error signal can be removed. without loss of information. The commonly used entropy coding methods are: run-length coding (RLE), Shannon coding, Huffman coding and arithmetic coding (arithmetic coding). Entropy coding is a kind of lossless source coding. The function of entropy coding is to remove the redundant information in the prediction error signal. In this process, no data information is lost. Since the source of the residual signal obeys geometric distribution, Rice coding is used to encode the residual signal.

Rice coding is a Huffman coding whose information source is Laplace distribution, and has only one parameter k. In fact, the prediction error signals in the decorrelation operation in the channel are all approximate to the Laplace probability density distribution. Rice encoding consists of three parts: ①sign bit, ②k-bit low-order code; ③reserved high-order bit. The first part of the codeword represents the symbol of e[n]; the second part contains the lower k significant bits of the binary code of |e[n]|, and the third part consists of N consecutive zeros, where N is |e[n ]|The binary representative value of the remaining significant digits, inserting 1 after N consecutive zeros as a separator.

Assuming that Rice is performed on integer n, the encoding steps are

(1) sign bit (1 represents positive, 0 represents negative)

(2)n/(2 ^k ) consecutive zeros

(3) separator bit 1

(4) The last k effective digits of n

We did two sets of experiments to compare the lossless compression coding algorithm described in this paper with MPEG ALS (RM22) and FLAC two lossless coding formats.

In the first set of experiments, we selected thirteen different music styles for lossless audio compression, and it has been proved that the encoder can achieve better compression performance for audio signals of different sound quality.

Comparison of compression results of different styles of audio files

In the second set of experiments, we selected a group of audio signals with different sampling rates and different quantization precisions to test our proposed coding system, in order to prove that the scheme can be better for various combinations of sampling rates and quantization precision. Effect.

Comparison of audio file compression results with different sampling rates and quantization precision

The above two groups of experiments prove that the method of the present invention can achieve better compression effects for music files of different styles, and for audio files of different sampling rates and quantization precisions, the method of the present invention can also obtain a compression effect comparable to that of the current mainstream audio lossless compression software. the result of.

Compared with prior art, positive effect of the present invention is:

1. The system can adaptively divide the signal into frames according to the correlation between the frames before and after the signal, so that the signals in one frame have a strong correlation, which brings benefits to the subsequent wavelet decomposition processing and LPC prediction.

2. This system adopts integer lifting wavelet transform, which avoids the error caused by truncation of processing data and filter coefficients.

3. The system optimizes the function with the best compression rate, and adjusts the wavelet series of the signal to the integer lifting according to different signals.

4. Use LPC predictive processing for the signal after wavelet decomposition to increase the compactness of the decomposed signal.

5. Coding the residual signal with a Rice code suitable for geometric distribution to further compress the signal.

Description of drawings

Figure 1: Encoder structure block diagram;

Figure 2: Block diagram of decoder structure;

Figure 3: Framing strategy;

Figure 4: Decomposition of lifting wavelet;

Figure 5: Reconstruction of lifting wavelet;

Figure 6: Integer wavelet transform and its inverse transform;

Figure 7: Forward predictor encoding diagram;

Figure 8: Forward predictor decoding graph.

Detailed ways

Below with reference to accompanying drawing of the present invention, describe preferred embodiment of the present invention in more detail, describe in detail how to realize the technical scheme of this invention:

The audio lossless coder/decoder system according to the method of the present invention includes two parts: a coder subsystem and a decoder subsystem. The structural block diagram of the system is shown in Figure 1 and Figure 2, wherein Figure 1 is a structural block diagram of the audio lossless compression coding subsystem, and Figure 2 is a structural block diagram of the audio lossless compression decoder subsystem. The system structure will be introduced in detail below in conjunction with the accompanying drawings.

1. Overall plan:

Encoder part: The structural block diagram of the encoder is shown in Figure 1: the audio file is first divided into several frames according to the framing strategy, and the frame information is included in the side information transmission; each frame after framing is processed separately, that is, the wavelet transform is first used to obtain each For the approximate signal and detail signal of a frame, the wavelet decomposition series is obtained according to the adaptive rule, and the decomposition series is also included in the side information; the approximate signal and the detail signal pass through the linear prediction module, and the residual signal obtained in the linear prediction module is entropy encoded , the LPC parameters are incorporated into the side information, and finally the code streams of each channel are multiplexed to form the final compressed code stream.

Decoder part: The structural block diagram of the decoder is shown in Figure 2: it is actually the inverse process of the encoder. By first decoding the side information, the entropy-encoded codebook is separated from it, and the residual after LPC prediction is solved, and the LPC parameter is used Solve the approximate signal and detail signal of wavelet decomposition, and then reconstruct the signal of each frame according to the information of wavelet decomposition series, and finally connect each frame sequentially according to the frame information, and obtain the original audio file without loss.

2. Framing strategy:

Since there are quite a lot of abrupt changes in the audio signal, if a fixed frame length is used for framing, the correlation between the obtained signals in each frame will be greatly affected, thereby reducing the compression rate. According to the correlation coefficients of adjacent frames, this scheme merges highly correlated signals into one frame. In this way, the compactness of wavelet transform and linear prediction will be improved, and higher compression efficiency can be obtained. Therefore, in this solution, the framing strategy shown in Figure 3 is adopted, so that signals with consistent characteristics can be processed within one frame.

First, calculate the correlation coefficient between the current frame and the previous frame with the minimum frame length as the unit. If the coefficient is less than the threshold, mark the frame and the previous frame as irrelevant frames and form a single frame. If the coefficient is greater than the threshold, it is considered The current frame is related to the previous frame, and the adjacent related frames are merged sequentially, but the maximum frame length does not exceed the set maximum frame length allowable value.

3. Integer lifting wavelet transform:

Lifting strategy: Swledens et al. have proved that any existing wavelet transform can be realized by cascading a limited number of lifting steps. In addition, the lifting transform implementation framework can be realized by integer wavelet transform. Figure 4 shows the most basic lifting scheme to realize wavelet transform, which contains three basic steps: separation, prediction and update.

Split: refers to separating x[n] into an odd sequence xo[n]=x[2n+1] and an even sequence xe[n]=x[2n] by downsampling. This separation is also called Lazy wavelet transform.

Prediction (predict): Generally speaking, there is a strong correlation between the odd and even sequences, and the even set can be used to predict the odd set (P is the prediction operator) to remove the redundancy between the data and obtain the high-frequency details of the signal.

d[n]=x _o [n]-P(x _e [n]) (1)

If the signal is locally smooth, the value of the prediction residual will be small.

Update: This step can obtain the low-frequency information of x[n], that is, the overview of the signal, or an approximate signal. The corresponding operation is to add the prediction residual d[n] to the even sequence xe[n] through the update operator U,

s[n]=x _e [n]+U(d _o [n]) (2)

The above is the decomposition algorithm of the lifting scheme, and the reconstruction algorithm of the lifting scheme can be derived from the properties of the lifting matrix as follows, including three steps of anti-update, anti-prediction, and combination, as shown in Figure 5

Undo update:

x _e [n]=s[n]-U(d[n]) (3)

Anti-prediction (undo predict):

x _o [n]=d[n]+P(x _e [n]) (4)

Synthesis (merge):

x[n]=Merge(x[2n+1]，x[2n]) (5)

Constructing different wavelet transforms depends on choosing different predictors and update operators. These operators can be constant coefficients (simple multiplication) or impulse responses of filters (convolution operation). The prediction operator corresponds to the scale function in the traditional wavelet transform, and different scale functions can be obtained by different forecast interpolation operators. Similarly, the update operator corresponds to the wavelet function in the traditional wavelet transform.

The traditional transform method, no matter it is fast Fourier transform or wavelet transform, the input signal is an integer, and the transformed coefficient is a floating-point number. There are rounding errors in the computer processing, and the lossless data compression cannot be realized.

On the other hand, the lifting scheme is used to calculate the wavelet transform, and the quantization operation can be added in the lifting process. Since the lifting matrix meets the requirement of complete reversibility, the wavelet transform from integer to integer can be realized. The specific situation is shown in the following formula: (Q is a quantization operator)

y(i)=x(i)+Q[αx(j)], y(k)=x(k), k≠i (6)

x(i)=y(i)-Q[αy(j)], x(k)=y(k), k≠i (7)

According to the above quantization and lifting steps, the implementation form of integer wavelet transform and its inverse transform can be obtained, as shown in Figure 6, each step of lifting is added with quantization operation, which ensures that the output of each step is an integer. First of all, any existing first-generation wavelet can be realized through a finite number of lifting structure cascades, and secondly, the gain factor can be 1 through four additional lifting transformations, so that the final output LP and BP are also integers , due to the reversible integer transformation at each step, it is obvious that the original signal can be accurately restored by LP and BP during the inverse transformation.

From the perspective of multi-resolution analysis or band-pass filter, wavelet decomposition is not limited to the above-mentioned one-level decomposition, and wavelet decomposition can be continued on the approximate signal after one-level decomposition to further remove its correlation, but due to Different signals have different frequency distributions, and the use of different decomposition series will have an impact on the compression result. The present invention uses different wavelet decomposition series to decompose the signal. According to the decomposed results, the series with the highest compression ratio is selected. And record the best decomposition series information into the side information.

4. LPC prediction:

This scheme adopts the method of forward prediction, and considers that the value of the discrete time signal at the current time point can be predicted by the linear combination of the values of the previous K points, and the expression is as follows:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

where k is the order of the predictor. If the prediction result of the predictor is close to the current signal, the variance of its residual error is closer to zero than the original signal, thus effectively reducing the encoding length. The structure of the forward predictor is shown in Figure 7, and its corresponding decoding process is shown in Figure 8.

The core problem of LPC forecasting is how to obtain the predictor coefficients according to the input signal. Assuming that the order of the predictor is p, it can be obtained from the Yule-Walker equation:

$\left(\begin{array}{ccccc}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& & <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& & <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& & <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>\end{array}\right)\left(\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\end{array}\right)<span\; class="notranslate">\; =</span>\left(\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right)<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Wherein, rx(i), i=0, 1, 2, . . . , p is the sample autocorrelation value, which can be estimated by the autocorrelation function of p points before the current sample point in the predictor. a1, a2, a3, ..., ap are predictor coefficients, and σ2 is the minimum error power of forward prediction. When the autocorrelation matrix is known, the predictor coefficients that minimize the error power are sought. This program uses the classic Levinson-Durbin algorithm to solve this coefficient.

Let the reflection coefficient am(m)=km, the recurrence equation of the coefficient obtained by the Levinson-Durbin algorithm is as follows:

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

a _m (k) = a _m-1 (k)-k _m a _m-1 (mk) (11)

${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

In this algorithm, the coefficients of each order are recursively obtained, so the appropriate predictor order and coefficients of each order can be compared and selected. Since km2 is a number greater than 0, there is always ρm<ρm-1, that is, as the iterative process proceeds, the prediction error will decrease step by step.

Since the prediction coefficients calculated according to the above optimal criteria are all floating-point numbers, the predictor reflection coefficients retained in the side information are quantized fixed-point numbers. Although certain optimization criteria are discarded, the complete reliability of the signal is guaranteed. Refactoring features.

5. Entropy coding

Since the residuals obey a certain distribution, entropy coding is generally applied to the residuals. In this scheme, the Rice code is used to code the residual signal. Rice encoding is suitable for encoding data whose distribution approximates a geometric distribution. Its distribution function is:

P _r {r _θ = p} = (1-θ)θ ^p , θ∈(0,1) (13)

But Rice encoding requires that the data must be positive. In order to meet this requirement, a mapping is first required on the residual signal, mapping negative values to positive values. The process is as follows:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

For a data p, divide the number by M (generally M=2n) at first to obtain a quotient q and the corresponding remainder r. Right now

r＝p-q·M (16)

Then the encoding method of the data is as follows: q bits of 1 are used to represent the quotient; 1 bit of 0 is used to distinguish the flag bit between the quotient and the remainder; [log2r] bits are used to represent the remainder r.

The appropriate M value in the formula is determined by the following method:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

Where the constant c1 = 0.97.

Although specific embodiments and drawings of the present invention are disclosed for the purpose of illustration, the purpose is to help understand the content of the present invention and implement it accordingly, but those skilled in the art can understand that: without departing from the present invention and the appended claims Various substitutions, changes and modifications are possible within the spirit and scope of . Therefore, the present invention should not be limited to what is disclosed in the preferred embodiments and drawings.

Claims (10)

1. An audio lossless compression coding method based on shaping wavelet transform, its steps are: 1) The framing module performs framing processing on the input audio signal, and incorporates the framing information into side information; 2) The integer wavelet transform module performs wavelet transform on each frame after framing to obtain approximate signal, detail signal and grading information, and incorporates grading information into side information; 3) The linear predictive coding module performs linear prediction on the approximate signal and the detail signal, obtains the residual signal and the LPC parameter, and incorporates the LPC parameter into the side information; 4) The entropy encoding module performs entropy encoding on the residual signal to obtain an entropy encoding stream, and simultaneously incorporates the codebook information of the entropy encoding into side information; 5) The bit stream forming module multiplexes the side information and the entropy coded stream to form a final compressed code stream. 2. The method according to claim 1, characterized in that the integer wavelet transform module is an integer lifting wavelet transform module. 3. The method according to claim 2, characterized in that the integer lifting wavelet transform module is an integer wavelet transform module of quadruple lifting transform. 4. The method according to claim 1 or 2, characterized in that the classification information is determined using an adaptive series selection method. 5 . The method according to claim 1 , wherein the framing module merges signals with high correlation into one frame according to the correlation coefficients of adjacent frames, and performs framing processing. 6 . 6. The method according to claim 5, wherein the framing module first calculates the correlation coefficient between the current frame and the previous frame in units of the minimum frame length; if the coefficient is less than the set threshold, the current frame Separately divided into a frame; otherwise, the current frame and the previous frame are marked as related frames, and then adjacent related frames are merged to form a frame. 7. The method according to claim 6, wherein a maximum frame length threshold is set, and when the frame length of the merged frame reaches the set maximum frame length threshold, a new frame is started for subdivision. 8. The method according to claim 1, characterized in that the entropy encoding module adopts a Rice code encoding method to entropy encode the residual signal. 9. An audio lossless compression decoding method based on shaping wavelet transform, the steps of which are: 1) The bit stream separation module decodes the side information from the compressed code stream, and separates the entropy coded codebook, LPC parameters, classification information and framing information from the side information; 2) The entropy decoding module performs entropy decoding on the compressed code stream according to the codebook information of the entropy encoding to obtain the residual signal; 3) The LPC reconstruction module uses the LPC parameters to solve the approximate signal and the detail signal of the wavelet decomposition from the residual signal; 4) The integer wavelet reconstruction module reconstructs the approximate signal and the detail signal according to the hierarchical information to obtain the signal of each frame; 5) The merging frame module connects each frame sequentially according to the framing information to obtain the original audio signal. 10. The method according to claim 9, characterized in that the integer wavelet reconstruction module is an integer lifting wavelet reconstruction module.

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