CN100517298C - Method for performing a domain transformation of a digital signal from the time domain into the frequency domain and vice versa - Google Patents

Abstract

A method for performing a domain transformation of a digital signal from the time domain into the frequency domain and vice versa, the method including performing the transformation by a transforming element, the transformation element comprising a plurality of lifting stages, wherein the transformation corresponds to a transformation matrix and wherein at least one lifting stage of the plurality of lifting stages comprises at least one auxiliary transformation matrix and a rounding unit, the auxiliary transformation matrix comprising the transformation matrix itself or the corresponding transformation matrix of lower dimension. The method further comprising performing a rounding operation of the signal by the rounding unit after the transformation by the auxiliary transformation matrix.

Description

Digital signal is transformed from the time domain to the method for frequency domain and reciprocal transformation thereof

The cross reference of related application

The application requires the U.S. Provisional Application No.60/507 of submission on September 29th, 2003, the U.S. Provisional Application No.60/507 that on September 29th, 210 and 2003 submitted to, 440 right of priority is incorporated herein by reference in full in this content with each, to be used for all purposes.

In addition, the following application of owning together is submitted to together simultaneously, introduces in full at this:

" Method for Performing a Domain Transformation of a DigitalSignal from the Time Domain into the Frequency Domain and vice Versa ", application attorney docket No.P100442, and

" Process and Device for Determining a Transforming Element for aGiven Transformation Function; Method and Device for Transforming aDigital signal from the Time Domain into the Frequency Domain and viceVersa and Computer Readable Medium ", application attorney docket No.P100452.

Background technology

The present invention relates to be used for digital signal is transformed from the time domain to frequency domain and the method from the frequency domain transform to the time domain.

The territory conversion, for example discrete cosine transform (DCT) is widely used in current signal Processing industry.In recent years, because its key player in lossless coding is used, the distortion that is called the DCT of integer DCT has attracted many research interest.Term " can't harm " and means that demoder can produce definitely duplicating of source signal according to bitstream encoded.

Described DCT is real-valued conversion.Even described input block only comprises integer, the IOB of described DCT can comprise the non-integer component.For easy, described input block is called as input vector, and IOB is called as output vector.If vector only comprises integer components, then this vector is called as integer vector.Contrast in DCT, described integer DCT produces the integer output vector according to the integer input vector.For same integer input vector, the integer output vector of integer DCT is in close proximity to the real output vector of DCT.Therefore, integer DCT keeps all good characteristics of described DCT when spectrum analysis.

The key property of described integer DCT is a reversibility.Reversibility means and has integral discrete cosine inverse transformation (IDCT), if make described integer DCT according to input vector xProduce output vector y, then described integer ID CT can be according to vector yRecover vector xSometimes integer DCT is also referred to as positive-going transition, and integer ID CT is called as reciprocal transformation or inverse transformation.

The conversion that is called integer improvement discrete cosine transform (IntMDCT) is suggested in recent years and is used in the ISO/IEC MPEG-4 audio compression.Described IntMDCT comes from its prototype---improvement discrete cosine transform (MDCT).H.S.Malvar disclosing in " Signal Processing With lappedTransforms " in 1992 realized MDCT effectively by utilizing the DCT-IV piece to come a series of Givens of cascade to rotate.What known is that the Givens rotation can be broken down into three lifting step, is used for integer is mapped to integer.For example, referring to R.Geiger, T.Sporer, J.Koller, K.Brandenburg in September calendar year 2001 " the AudioCoding based on Integer Transforms " in the 111st meeting of USA New York AES.

Therefore, the realization of IntMDCT depends on effective realization of integer DCT-IV.

By utilizing three lifting step to replace each Givens rotation, can directly change integer transform from its prototype.Owing to there is the operation that rounds up in each lifting step, the number of times that always rounds up of integer transform is 3 times of Givens number of revolutions of prototype conversion.For discrete trigonometric transforms (for example discrete Fourier transform (DFT) (DFT) or discrete cosine transform (DCT)), the number of times of related Givens rotation is generally Nlog ₂The N level, wherein N is a described size, i.e. the amount of the data symbol that is divided into of the described digital signal that comprises in each piece.Therefore, for the family of the integer transform of direct conversion, the described number of times that always rounds up also is Nlog ₂The N level.Because described rounding up, integer transform only is similar to its floating-point prototype.Described approximate error increases along with the increase of the number of times that rounds up.

Therefore, needed is to be used for coming digital signal is carried out the system and method for territory conversion in more efficiently mode.

Summary of the invention

The invention provides and be used for digital signal is carried out the territory conversion, thus the system and method that in same operation, simultaneously two data input blocks is carried out the territory conversion.This configuration has reduced the number of times of the operation that effectively rounds up, and therefore reduces approximate error.

In one embodiment of the invention, present a kind of method of the present invention, this method uses transforming function transformation function that digital signal is transformed from the time domain to frequency domain and from the frequency domain transform to the time domain.Described transforming function transformation function comprises transformation matrix, and described digital signal comprises a plurality of data symbols that are grouped into a plurality of, and each piece comprises the data symbol of predetermined number.Described method comprises utilizes a conversion unit two pieces of changed digital signal usually, wherein said conversion element is corresponding to the block diagonal matrix that comprises two submatrixs, wherein each submatrix comprises transformation matrix, and the conversion element comprises a plurality of liftings levels (liftingstage), and wherein each promotes level and comprises and utilize householder transformation and the unit that rounds up comes the piece of digital signal is handled.

When watching according to the detailed description of the drawings and specific embodiments, these and other features of the present invention will better be understood.

Description of drawings

Fig. 1 shows the architecture of audio coder according to an embodiment of the invention;

Fig. 2 shows the architecture of audio decoder according to an embodiment of the invention, and it is corresponding to the audio coder shown in Fig. 1;

Fig. 3 shows the process flow diagram of the embodiment of the method according to this invention;

Fig. 4 has illustrated the embodiment of the method according to this invention, and it uses DCT-IV as transforming function transformation function;

Fig. 5 has illustrated the algorithm that is used for according to the inverse transformation of the embodiment of method of the present invention illustrated in fig. 4;

Fig. 6 shows the architecture of image archiving system according to an embodiment of the invention;

Fig. 7 shows the direct transform scrambler and the inverse transformation scrambler of the performance of the system and method that is used to estimate described proposition.

Detailed Description Of The Invention

Fig. 1 shows the architecture of audio coder 100 according to an embodiment of the invention.Described audio coder 100 comprises based on the conventional perception base layer coder (perceptual base layer coder) of improving discrete cosine transform (MDCT) and improves the harmless enhanced encoder (enhancement coder) of discrete cosine transform (IntMDCT) based on integer.

For example, will provide and carry out digitized sound signal 109 by microphone 110 and offer audio coder 100 by A/D converter 111.Described sound signal 109 comprises a plurality of data symbols.Described sound signal 109 is divided into a plurality of, and wherein each piece comprises a plurality of data symbols of digital signal, and by improving discrete cosine transform (MDCT) equipment 101 each piece is carried out conversion.Described MDCT coefficient is quantized by means of sensor model 102 by quantizer 103.Described sensor model is controlled described quantizer 103 according to a kind of like this mode, makes that the audio distortions that is produced by quantization error is low.The MDCT coefficient that has been quantized by 104 pairs of bitstream encoder is encoded subsequently, and this bitstream encoder 104 produces (perceptually coded) output bit flow 112 of the perceptual coding that diminishes.

Described bitstream encoder 104 is utilized such as the standard method of Huffman coding or the distance of swimming (Run-Length) coding and is nondestructively compressed its input to produce an output, and the mean bit rate of this output will be lower than the mean bit rate of its input.Described input audio signal 109 also is transported in the IntMDCT equipment 105 that produces the IntMDCT coefficient.The MDCT of quantification coefficient by the output of quantizer 103 is used to predict described IntMDCT coefficient.The described MDCT coefficient that quantized is transported in contrary-quantizer 106, and the described output MDCT coefficient of non-quantification (recovered or) is transported to the unit 107 that rounds up.

The described unit that rounds up is rounded up to a round values with the described MDCT coefficient that provides, and carries out entropy coding by the IntMDCT coefficient of 108 couples of remnants of entropy coder, and the IntMDCT coefficient of described remnants is the poor of round values MDCT and IntMDCT coefficient.Described entropy coder is similar to bitstream encoder 104, nondestructively reduces the mean bit rate of its input, and produces the harmless bit stream 113 that strengthens.Described harmless enhancing bit stream 113 and perceptual coding bit stream 112 carry essential information together, have the input audio signal 109 of least error with reconstruct.

Fig. 2 shows the architecture of the audio decoder 200 that comprises embodiments of the invention, and it is corresponding to the audio coder shown in Fig. 1 100.Described perceptual coding bit stream 207 is provided for bit stream decoding device 201, and the inverse operation of the operation of the bitstream encoder 104 of these bit stream decoding device 201 execution graphs 1 produces decoded bit stream.Described decoded bit stream is provided for contrary-quantizer 202, and the output of this contrary-quantizer 202 (the MDCT coefficient that has recovered) is provided for inverse discrete cosine transform (anti-MDCT) equipment 203 that improves.Therefore, obtain the perceptual coding sound signal 209 of reconstruct.

Described harmless enhancing bit stream 208 is provided for entropy decoder 204, and the inverse operation of the operation of the entropy coder 108 in these entropy decoder 204 execution graphs 1 produces corresponding remaining IntMDCT coefficient.Output by 205 pairs of contrary-quantizers 202 of the equipment of rounding up rounds up, to produce round values MDCT coefficient.Described round values MDCT coefficient is added to described remaining IntMDCT coefficient, produces described IntMDCT coefficient thus.At last, improve 206 pairs of described IntMDCT coefficients of inverse discrete cosine transform (anti-IntMDCT) equipment by described integer and carry out described integer improvement inverse discrete cosine transform, to produce the harmless encoded audio signal 210 of described reconstruct.

Fig. 3 shows the process flow diagram 300 of the embodiment of the method according to this invention, and this method use DCT-IV is as conversion and use three to promote level, and first promotes level 301, the second lifting level the 302 and the 3rd promotes level 303.This method is preferably used in the anti-IntMDCT equipment 206 of the IntMDCT of Fig. 1 equipment 105 and Fig. 2, to finish IntMDCT and anti-IntMDCT respectively.In Fig. 3, x ₁ With x ₂ Be respectively first and second of digital signal. zBe M signal, and y ₁ With y ₂ Be respectively first and second corresponding output signal with digital signal.

As mentioned above, the DCT-IV algorithm is played an important role in lossless audio coding.

The transforming function transformation function of described DCT-IV comprises transformation matrix C _N ^IV According to this embodiment of the invention, described conversion element is corresponding to the block diagonal matrix that comprises two pieces, and wherein each piece comprises transformation matrix C _N ^IV

Therefore, in this embodiment, the transformation matrix corresponding with conversion element according to the present invention is:

$\left[\begin{array}{cc}& \underset{\‾}{C_N^{\mathrm{IV}}}\\ \underset{\‾}{C_N^{\mathrm{IV}}}& \end{array}\right]$

In the context of this embodiment, C _N ^IV Henceforth should be known as transformation matrix.

In this embodiment of the present invention, promote the number of matrix, and the number of the lifting level in the conversion element is 3, wherein DCT-IV is a transforming function transformation function.

The DCT-IV quilt of the real list entries x of N point (n) is as giving a definition:

$y\left(m\right)=\sqrt{\frac{2}{N}}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}x\left(n\right)\cos \left(\frac{(m+1/2)(n+1/2)\mathrm{\π}}{N}\right)$ m，n＝0，1，...，N-1 (1)

Suppose C _N ^IV Be the transformation matrix of DCT-IV, that is,

$\underset{\‾}{C_N^{\mathrm{IV}}}=\sqrt{\frac{2}{N}}{\left[\cos \left(\frac{(m+1/2)(n+1/2)\mathrm{\π}}{N}\right)\right]}_{m,n=\mathrm{0,1},..,N-1}---\left(2\right)$

For anti-DCT-IV matrix, following relation is set up,

${\left(\underset{\‾}{C_N^{\mathrm{IV}}}\right)}^{-1}=\underset{\‾}{C_N^{\mathrm{IV}}}---\left(3\right)$

Especially, matrix C _N ^IV Be from inverse matrix (involutory).

When x=[x (n)] _{N=0,1 ..., N-1}With y=[y (m)] _{M=0,1 ..., N-1}The time, equation (1) can be expressed as

$\underset{\‾}{y}=\underset{\‾}{C_N^{\mathrm{IV}}}\underset{\‾}{x}---\left(4\right)$

Now, suppose x ₁ With x ₂ It is two Integer N * 1 column vector.Described column vector x ₁ With x ₂ Corresponding to two pieces of digital signal,, utilize a conversion element that these two pieces are carried out conversion according to the present invention. x ₁ With x ₂ The DCT-IV conversion be respectively y ₁ With y ₂

$\underset{\‾}{y_1}=\underset{\‾}{C_N^{\mathrm{IV}}{x}_1}---\left(5\right)$

$\underset{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">y</figure-callout>}}_2}=\underset{\&OverBar;}{C_N^{\mathrm{IV}}{x}_2}---\left(6\right)$

Merge (5) and (6):

$\left[\begin{array}{c}\underset{\&OverBar;}{y_1}\\ \underset{\&OverBar;}{y_2}\end{array}\right]=\left[\begin{array}{cc}\underset{\&OverBar;}{C_N^{\mathrm{IV}}}& \\ & \underset{\&OverBar;}{C_N^{\mathrm{IV}}}\end{array}\right]\left[\begin{array}{c}\underset{\&OverBar;}{x_1}\\ \underset{\&OverBar;}{x_2}\end{array}\right]---\left(7\right)$

Above-mentioned diagonal matrix is the block diagonal matrix according to conversion element correspondence of the present invention.

If utilize simple algebraically correction to change above-mentioned equation, for example cause

$\left[\begin{array}{c}\underset{\&OverBar;}{y_1}\\ \underset{\&OverBar;}{y_2}\end{array}\right]=\left[\begin{array}{cc}& \underset{\&OverBar;}{C_N^{\mathrm{IV}}}\\ \underset{\&OverBar;}{C_N^{\mathrm{IV}}}& \end{array}\right]\left[\begin{array}{c}\underset{\&OverBar;}{x_2}\\ \underset{\&OverBar;}{x_1}\end{array}\right]---\left(8\right)$

Then still within the scope of the invention.

Suppose T _2N Be anti-(counter) diagonal matrix in (8), then

$\underset{\&OverBar;}{T_{2N}}=\left[\begin{array}{cc}& \underset{\&OverBar;}{C_N^{\mathrm{IV}}}\\ \underset{\&OverBar;}{C_N^{\mathrm{IV}}}& \end{array}\right]---\left(9\right)$

Matrix T _2N Can be by following decomposition

$\underset{\&OverBar;}{T_{2N}}=\left[\begin{array}{cc}& \underset{\&OverBar;}{C_N^{\mathrm{IV}}}\\ \underset{\&OverBar;}{C_N^{\mathrm{IV}}}& \end{array}\right]=\left[\begin{array}{cc}\underset{\&OverBar;}{I_N}& \\ -\underset{\&OverBar;}{C_N^{\mathrm{IV}}}& \underset{\&OverBar;}{I_N}\end{array}\right]\left[\begin{array}{cc}-\underset{\&OverBar;}{I_N}& \underset{\&OverBar;}{C_N^{\mathrm{IV}}}\\ & \underset{\&OverBar;}{I_N}\end{array}\right]\left[\begin{array}{cc}\underset{\&OverBar;}{I_N}& \\ \underset{\&OverBar;}{C_N^{\mathrm{IV}}}& \underset{\&OverBar;}{I_N}\end{array}\right]---\left(10\right)$

Wherein I _N It is the unit matrix of N * N.

Use the characteristic of the DCT-IV in the equation (3) can easily verify equation (10).Use equation (10), equation (8) can be expressed as

$\left[\begin{array}{c}\underset{\&OverBar;}{y_1}\\ \underset{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">y</figure-callout>}}_2}\end{array}\right]=\left[\begin{array}{cc}\underset{\&OverBar;}{I_N}& \\ -\underset{\&OverBar;}{C_N^{\mathrm{IV}}}& \underset{\&OverBar;}{I_N}\end{array}\right]\left[\begin{array}{cc}-\underset{\&OverBar;}{I_N}& \underset{\&OverBar;}{C_N^{\mathrm{IV}}}\\ & \underset{\&OverBar;}{I_N}\end{array}\right]\left[\begin{array}{cc}\underset{\&OverBar;}{I_N}& \\ \underset{\&OverBar;}{C_N^{\mathrm{IV}}}& \underset{\&OverBar;}{I_N}\end{array}\right]\left[\begin{array}{c}\underset{\&OverBar;}{x_2}\\ \underset{\&OverBar;}{x_1}\end{array}\right]---\left(11\right)$

Three in the equation (11) promote matrix and promote level corresponding to three among Fig. 3.

According to equation (11), can obtain following integer DCT-IV algorithm, this algorithm uses a conversion unit usually to calculate two integer DCT-IV.

Fig. 4 illustration the embodiment of the method according to this invention, this method uses DCT-IV as transforming function transformation function.This embodiment is used in the audio coder 100 shown in Fig. 1, to realize IntMDCT.Be similar among Fig. 3, x ₁ With x ₂ Be respectively two pieces of described supplied with digital signal. zBe M signal, and y ₁ With y ₂ It is respectively the relevant block of output signal.

Illustrative three promote level corresponding to three in the equation (11) lifting matrixes among Fig. 4.

As shown in Figure 4, utilize following proposal to determine that time domain arrives the frequency domain integer transform:

In the first order 401, it is right to utilize the DCT-IV conversion x ₂ Carry out conversion 402, the DCT-IV coefficient is rounded up 403.To be added to through the DCT-IV coefficient after rounding up subsequently x ₁ 404.Thus, produce M signal zTherefore, M signal zSatisfy equation:

In the second level 405, it is right to utilize the DCT-IV conversion zCarry out conversion 406, the DCT-IV coefficient is rounded up 407.Deduct the DCT-IV coefficient after process rounds up subsequently x ₂ Thus, produce output signal y ₁ Therefore, output signal y ₁ Satisfy equation:

In the third level 409, it is right to utilize the DCT-IV conversion y ₁ Carry out conversion 410, the DCT-IV coefficient is rounded up 411.Subsequently from zIn deduct through the DCT-IV coefficient after rounding up.Thus, produce output signal y ₂ Therefore, output signal y ₂ Satisfy equation:

Wherein Represent to round up operation.

Fig. 5 has illustrated the algorithm of inverse transformation of the embodiment of the method according to this invention, and this method uses DCT-IV as transforming function transformation function.This embodiment is used in the audio decoder 200 shown in Fig. 2, to realize anti-IntMDCT.Illustrative algorithm is the inverse operation of illustrative algorithm among Fig. 4 among Fig. 5.The expression of unlike signal y ₁ , y ₂ , x ₁ , x ₂ And zBe selected as corresponding to the expression among Fig. 4.

As shown in Figure 5, utilize following method to determine the integer transform of frequency domain to time domain:

In the first order 501, it is right to utilize the DCT-IV conversion y ₁ Carry out conversion 502, the DCT-IV coefficient is rounded up 503.To be added to through the DCT-IV coefficient after rounding up subsequently y ₂ 504.Thus, produce M signal zTherefore, M signal zSatisfy equation:

In the second level 505, it is right to utilize the DCT-IV conversion zCarry out conversion 506, the DCT-IV coefficient is rounded up 507.Deduct the DCT-IV coefficient after process rounds up subsequently y ₁ Thus, produce signal x ₂ Therefore, signal x ₂ Satisfy equation:

In the third level 509, it is right to utilize the DCT-IV conversion x ₂ Carry out conversion 510, the DCT-IV coefficient is rounded up 511.Subsequently from zIn deduct through the DCT-IV coefficient after rounding up.Thus, produce signal x ₁ Therefore, signal x ₁ Satisfy equation:

As can be seen, be according to equation (12a) contrary to the algorithm of (12c) according to the algorithm of equation (13a) to (13c).Therefore, if use in the illustrative encoder in Fig. 1 and Fig. 2, then described algorithm is provided for the method and apparatus of lossless audio coding.

In the embodiments of the invention of following explanation, said method is used for image archiving system.

Equation (12a) to (12c) and (13a) further illustrate to (13c) in order to calculate the integer DCT-IV of two N * N, needs rounding up and the addition of three N * 1 of the DCT-IV of three N * N, three N * 1.Therefore, for the integer DCT-IV of a N * N, mean value is:

RC(N)＝1.5N (14)

$\mathrm{AC}\left(N\right)=1.5\mathrm{AC}\left(C_N^{\mathrm{IV}}\right)+1.5N---\left(15\right)$

Wherein RC (.) is total number of times that rounds up, and AC (.) is the total degree of algorithm operating.Compare with the integer DCT-IV algorithm of direct conversion, the integer DCT-IV algorithm of described proposition with RC from Nlog ₂The N order of magnitude reduces to N.

Shown in equation (15), the complexity of the integer DCT-IV algorithm of described proposition is more than the complexity of DCT-IV algorithm about 50%.Yet if also consider RC, the combination complexity (AC+RC) of the algorithm of described proposition does not substantially exceed the complexity of the integer arithmetic of direct conversion.The Accurate Analysis of the complexity of described algorithm depends on employed DCT-IV algorithm.

As shown in Figures 4 and 5, the integer DCT-IV algorithm of described proposition modularization simply and structurally.In its DCT-IV computing block, it can use any existing DCT-IV algorithm.The algorithm of described proposition is suitable for the application of requirement IntMDCT, for example expands in 3 reference models 0 at the MPEG-4 audio frequency.

Fig. 6 shows the architecture of image archiving system according to an embodiment of the invention.

In Fig. 6, image source 601, for example camera provides analog picture signal.By A/D converter 602 this picture signal is handled, so that the corresponding digital picture signal to be provided.Carry out lossless coding by 603 pairs of these data image signals of lossless image scrambler, it comprises the conversion from the time domain to the frequency domain.In this embodiment, time domain is corresponding to the coordinate space of described image.Picture signal behind the described lossless coding is stored in the memory device 604, for example hard disk or DVD.When the described image of needs, picture signal from described memory device 604 behind the described lossless coding of taking-up, and provide it to the lossless image demoder 605 corresponding with lossless image scrambler 603, picture signal behind 605 pairs of lossless codings of this lossless image demoder is decoded, and the described original image signal of reconstruct and loss of data can not occur.

For example, be that the Error Graph of semiconductor wafer and must being stored is come being used under the situation with post analysis at described image, this of picture signal kind of harmless filing is important.

In this embodiment of the present invention, Fig. 3 embodiment of illustrative method in Fig. 5 is used for lossless image scrambler 603 and lossless image demoder 605.As mentioned above, Fig. 3 the embodiment of illustrative method in Fig. 5 provide a kind of reversible conversion, and therefore a kind of lossless image Methods for Coding that is used for is provided especially.

The method according to this invention is not limited to the AV signal.Can also utilize the method according to this invention to come other digital signals of for example vision signal are carried out conversion.

Below, the another embodiment that is used for digital signal is transformed from the time domain to frequency field and the method from the frequency domain transformation to the time domain according to the present invention is made an explanation.

In this embodiment of the present invention, the conversion of described territory is a dct transform, and block size N is a certain integer thus.In one embodiment, N is 2 power.

Suppose C _N ^IIBe N * N transformation matrix (being also referred to as II type DCT) of DCT:

$\begin{array}{c}{C}_N^{\mathrm{II}}=\sqrt{2/N}\left[k_m\cos (m(n+1/2)\mathrm{\&pi;}/N)\right]\\ m,n=\mathrm{0,1},...,N-1\end{array}---\left(16\right)$

Wherein

$k_m=\left\{\begin{array}{ccc}1/\sqrt{2}& \mathrm{if}& m=0\\ 1& \mathrm{if}& m\&NotEqual;0\end{array}\right.---\left(17\right)$

And N is a transform size.M and n are matrix index (index).

Suppose C _N ^IVBe N * N transformation matrix of the DCT of IV type DCT, as above definition:

$\begin{array}{c}{C}_N^{\mathrm{IV}}=\sqrt{2/N}\left[\cos ((m+1/2)(n+1/2)\mathrm{\&pi;}/N)\right]\\ m,n=\mathrm{0,1},...,N-1\end{array}---\left(18\right)$

As above, use a plurality of lifting matrixes, in this embodiment, described lifting matrix is the 2N * 2N matrix with following form:

$L_{2N}=\left[\begin{array}{cc}\&PlusMinus;I_N& A_N\\ O_N& \&PlusMinus;I_N\end{array}\right]---\left(19\right)$

I wherein _NBe the unit matrix of N * N, O _NBe the null matrix of N * N, and A _NIt is N * N matrix arbitrarily.

Promote matrix L for each _2NRealize promoting the mapping of the reversible integer of level to integer according to the mode identical with 2 * 2 lifting step described in the following list of references of introducing, described list of references is the I.Daubechies of Lucent Technologies's Bell Laboratory and W.Sweldens at Tech.Report (technical report) " Factoring Wavlet Transforms into Lifting Steps " in 1996.Only difference is to round up and is applied to vector, rather than is applied to single variable.

In the foregoing description of other embodiment, how described in detail is lifting level of lifting matrix realization, therefore, will omit the explanation of the lifting level corresponding with promoting matrix below.

As can be seen, L _2NTransposition L _2N ^TAlso be to promote matrix.

In this embodiment, described conversion element is corresponding to matrix T _2N, it is defined as 2N * 2N matrix in the following manner:

$T_{2N}=\left[\begin{array}{cc}{C}_N^{\mathrm{IV}}& O_N\\ O_N& C_N^{\mathrm{IV}}\end{array}\right]---\left(20\right)$

With matrix T _2NBe decomposed into the lifting matrix and have following form:

T _2N＝P3·L8·L7·L6·P2·L5·L4·L3·L2·L1·P1 (21)

Explain the matrix of the right-hand side of forming above-mentioned equation below.

P1 is first permutation matrix that is provided by following equation

$P1=\left[\begin{array}{cc}{O}_N& D_N\\ J_N& O_N\end{array}\right]---\left(22\right)$

J wherein _NBe to draw matrix (counter index matrix) by counterclaim given below

And D _NBe that wherein diagonal element alternately is 1 and the diagonal matrix of N * N of-1:

P2 is second permutation matrix, and its example is produced by following MATLAB script:

As an example, when N was 4, P2 was 8 * 8 matrixes, following providing

$\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">P</figure-callout>}2=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 1& 0& 0& 0& 0\end{array}\right]$ N=4 (25) wherein

P3 is the 3rd permutation matrix, and its example is produced by following MATLAB script:

As an example, when N was 4, P3 was 8 * 8 matrixes, following providing

$P3=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0\end{array}\right]$ N=4 (26) wherein

L1 is the first lifting matrix

$L1=\left[\begin{array}{cc}{I}_N& O_N\\ {Z1}_N& I_N\end{array}\right]---\left(27\right)$

Z1 wherein _NBe that the following N that provides * N opposes the angular moment battle array:

L2 is the second lifting matrix

$\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">L</figure-callout>}2=\left[\begin{array}{cc}{I}_N& {Z2}_N\\ O_N& I_N\end{array}\right]---\left(29\right)$

Z2 wherein _NBe that the following N that provides * N opposes the angular moment battle array:

L3 is the 3rd lifting matrix

$L3=\left[\begin{array}{cc}{I}_N& O_N\\ {Z3}_N& I_N\end{array}\right]---\left(31\right)$

Wherein

${Z3}_N=\sqrt{2}{C}_N^{\mathrm{IV}}+I_N+{Z1}_N---\left(32\right)$

L4 is the 4th lifting matrix

$L4=\left[\begin{array}{cc}-I_N& {Z4}_N\\ O_N& I_N\end{array}\right]---\left(33\right)$

Wherein

${Z4}_N=C_N^{\mathrm{IV}}/\sqrt{2}---\left(34\right)$

L5 is the 5th lifting matrix

$L5=\left[\begin{array}{cc}{I}_N& O_N\\ {Z5}_N& I_N\end{array}\right]---\left(35\right)$

Wherein

${Z5}_N=-(\sqrt{2}{C}_N^{\mathrm{IV}}+I_N)---\left(36\right)$

L6 is the 6th lifting matrix

$L6=\left[\begin{array}{cc}{I}_N& O_N\\ {Z6}_N& I_N\end{array}\right]---\left(37\right)$

Z6 wherein _NBe that the following N that provides * N opposes the angular moment battle array:

L7 is the 7th lifting matrix

$L7=\left[\begin{array}{cc}{I}_N& {Z7}_N\\ O_N& I_N\end{array}\right]---\left(39\right)$

Z7 wherein _NBe that the following N that provides * N opposes the angular moment battle array:

L8 is the 8th lifting matrix:

L8＝L6 (41)

Thus, cause factorization as shown in (42):

T _2N＝P3·L8·L7·L6·P2·L5·L4·L3·L2·L1·P1 (42)

Wherein P1, P2 and P3 are three permutation matrixes, L _jBe eight and promote matrix, wherein j from 1 to 8.

Promote matrix L 3, L4 and L5 and comprise the householder transformation matrix, in this case, it is transformation matrix C _N ^IVSelf.

According to equation (42), can for size two input signal computes integer DCT of N * 1.

Because equation (42) provides a description the lifting matrix factorization of DCT-IV transform domain, so it promotes the territory conversion that matrix can be used for calculating the input signal that is applied according to the mode that illustrates here.

Can obtain equation (42) in the following manner.

Can use the following open following decomposition that obtains, the disclosure is Wang, Zhongde is at the IEEE in 1985 October Transactions on Acoustic, Speech and Signal Processing (acoustics, voice and signal Processing journal), Vol.ASSP-33, " the On Computingthe Discrete Fourier and Cosine Transforms " that delivers on the No.4.

$C_N^{\mathrm{IV}}={\left(B_N\right)}^T\&CenterDot;{\left(P_N\right)}^T\&CenterDot;\left[\begin{array}{cc}{C}_{N/2}^{\mathrm{II}}& \\ & \stackrel{\stackrel{\&OverBar;}{\&OverBar;}}{S_{N/2}^{\mathrm{II}}}\end{array}\right]\&CenterDot;T_N---\left(43\right)$

$={\left(B_N\right)}^T\&CenterDot;{\left(P_N\right)}^T\&CenterDot;\left[\begin{array}{cc}{C}_{N/2}^{\mathrm{II}}& \\ & C_{N/2}^{\mathrm{II}}\end{array}\right]\&CenterDot;P_{\mathrm{DJ}}\&CenterDot;T_N$

Be known, S wherein _N/2 ^IIThe transformation matrix of expression II type discrete sine transform.

$P_{\mathrm{DJ}}=\left[\begin{array}{cc}I& \\ & D\&CenterDot;J\end{array}\right]$

P _N It is the following N that provides * N permutation matrix

$\underset{\&OverBar;}{P_N}=\left[\begin{array}{cc}\underset{\&OverBar;}{I_{N/2}}& \\ & \underset{\&OverBar;}{J_{N/2}}\end{array}\right]---\left(44\right)$

With

Equation (85) can merge with following equation

$C_N^{\mathrm{IV}}=R_{\mathrm{PO}}\&CenterDot;\left[\begin{array}{cc}{C}_{N/2}^{\mathrm{IV}}& \\ & C_{N/2}^{\mathrm{IV}}\end{array}\right]\&CenterDot;R_{\mathrm{PR}}\&CenterDot;P_D\&CenterDot;P_{\mathrm{EO}}---\left(45\right)$

P wherein _EOBe even odd permutation matrix,

$\underset{\&OverBar;}{R_{\mathrm{pr}}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}\underset{\&OverBar;}{I_{N/2}}& \underset{\&OverBar;}{I_{N/2}}\\ \underset{\&OverBar;}{I_{N/2}}& \underset{\&OverBar;}{{-I}_{N/2}}\end{array}\right]$

R _POEqual T _N,

${\underset{\&OverBar;}{P}}_D=\left[\begin{array}{cc}\underset{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="I\; N"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">I</figure-callout>}}_{\frac{N}{}}}& \\ & \underset{\&OverBar;}{{\mathrm{<figure-callout\; id="2"\; label="D\; N"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\frac{N}{}}}\end{array}\right]$

Be converted to (46) back at transposition equation (45):

$C_N^{\mathrm{IV}}={\left(P_{\mathrm{EO}}\right)}^T\&CenterDot;{\left(P_D\right)}^T\&CenterDot;R_{\mathrm{PR}}\&CenterDot;\left[\begin{array}{cc}{C}_{N/2}^{\mathrm{IV}}& \\ & C_{N/2}^{\mathrm{IV}}\end{array}\right]\&CenterDot;{\left(R_{\mathrm{PO}}\right)}^T---\left(46\right)$

$={\left(P_{\mathrm{EO}}\right)}^T\&CenterDot;{\left(P_D\right)}^T\&CenterDot;\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{C}_{N/2}^{\mathrm{IV}}& C_{N/2}^{\mathrm{IV}}\\ C_{N/2}^{\mathrm{IV}}& -C_{N/2}^{\mathrm{IV}}\end{array}\right]\&CenterDot;{\left(R_{\mathrm{PO}}\right)}^T$

Combination equation (43) and (46) obtains:

$\left[\begin{array}{cc}{C}_{N/2}^{\mathrm{II}}& \\ & C_{N/2}^{\mathrm{II}}\end{array}\right]=P_N\&CenterDot;B_N\&CenterDot;{\left(P_{\mathrm{EO}}\right)}^T{\left(P_D\right)}^T\&CenterDot;\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{C}_{N/2}^{\mathrm{IV}}& C_{N/2}^{\mathrm{IV}}\\ C_{N/2}^{\mathrm{IV}}& -C_{N/2}^{\mathrm{IV}}\end{array}\right]\&CenterDot;{\left(R_{\mathrm{PO}}\right)}^T\&CenterDot;T_N\&CenterDot;{\left(P_{\mathrm{DJ}}\right)}^T---\left(47\right)$

$=P_3\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">R</figure-callout>}}_2\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">P</figure-callout>}}_2\&CenterDot;\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{C}_{N/2}^{\mathrm{IV}}& C_{N/2}^{\mathrm{IV}}\\ C_{N/2}^{\mathrm{IV}}& -C_{N/2}^{\mathrm{IV}}\end{array}\right]\&CenterDot;R_1\&CenterDot;P_1$

Wherein:

P ₁＝(P _DJ) ^T

P ₂＝(P _EO) ^T·(P _D) ^T＝(P _D·P _EO) ^T

P ₃＝P _N

R ₁＝(R _PO) ^T·T _N

R ₂＝B _N

According to equation (47), can easily obtain equation (42).

In this embodiment, the calculating of territory conversion only needs 4N the operation that rounds up, as describing now.

Suppose that α (*) is the number of times of real addition, μ (*) is the number of times of real multiplication, and γ (*) is the real number of times that rounds up.IntDCT algorithm for described proposition can obtain:

α(IntDCT)＝11N+3α(DCT-IV)

μ(IntDCT)＝9N+3μ(DCT-IV)

γ(IntDCT)＝8N

Because the IntDCT algorithm of described proposition is handled together to them, so The above results is at two pieces of data sampling.Thus, for a piece of data sampling, the number of times of described calculating is halved, and it is

α ₁(IntDCT)＝5.5N+1.5α(DCT-IV)

μ ₁(IntDCT)＝4.5N+1.5μ(DCT-IV)

γ ₁(IntDCT)＝4N

α wherein ₁, μ ₁And γ ₁Be respectively number of times and the real number of times that rounds up at the number of times of the real addition of a piece of sampling, real multiplication.

Calculate for DCT-IV, can use the list of references H.S.Malvar that is incorporating into, MA.Artech House published the algorithm of describing on the 199-201 page or leaf of " Signal Processing With lappedTransforms " based on FFT, according to this algorithm by Norwood in 1992

α(DCT-IV)＝1.5Nlog ₂ N

μ(DCT-IV)＝0.5Nlog ₂ N+N

Therefore obtain:

α ₁(IntDCT)＝2.25Nlog ₂ N+5.5N

μ ₁(IntDCT)＝0.75Nlog ₂ N+6N

Below, the another embodiment that is used for digital signal is transformed from the time domain to frequency displacement and the method from the frequency domain transformation to the time domain according to the present invention is made an explanation.

In this embodiment, discrete fast fourier transform (FFT) is used as the territory conversion.

Suppose that F is the N * N transformation matrix with normalized FFT,

$\begin{array}{c}F=\sqrt{\frac{1}{N}}\left[\exp \left(\frac{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20048003505500341.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;mn}}{N}\right)\right]\\ m,n=\mathrm{0,1},...,N-1\end{array}---\left(48\right)$

Wherein N is a transform size.M and n are matrix indexes.

In this embodiment, dimension is that the permutation matrix P of N * N is the matrix that comprises index 0 or 1.After itself and N * 1 n dimensional vector n (matrix representation of input signal) were multiplied each other, the order of the element in the described vector was changed.

In this embodiment, promote 2N * 2N matrix that matrix is defined as having following form.

$L=\left[\begin{array}{cc}{P}_1& A\\ O& P_2\end{array}\right]---\left(49\right)$

P wherein ₁And P ₂Be two permutation matrixes, O is N * N null matrix, and A is any N * N matrix.For promoting matrix L, realize that according to the mode identical reversible integer shines upon to integer with 2 * 2 lifting step in the list of references of the above-mentioned I.Daubechies that incorporates into.Yet as mentioned above, will round up is applied to vector rather than is applied to single variable.It is evident that the transposition LT of described L promotes matrix.

In addition, suppose that T is 2N * 2N transformation matrix:

$T=\left[\begin{array}{cc}O& F\\ F& O\end{array}\right]---\left(50\right)$

Therefore, improved transformation matrix T (and the conversion of correspondingly described territory itself) can be represented as and promote matrix factor decomposed form:

$T=\left[\begin{array}{cc}I& O\\ -Q\&CenterDot;F& I\end{array}\right]\&CenterDot;\left[\begin{array}{cc}-Q& F\\ O& I\end{array}\right]\&CenterDot;\left[\begin{array}{cc}I& O\\ F& I\end{array}\right]---\left(51\right)$

Wherein I is the unit matrix of N * N, and Q is the permutation matrix of the following N * N that provides

$Q=\left[\begin{array}{cc}1& O_{1\mathrm{xN}-1}\\ O_{N-1x1}& J\end{array}\right]---\left(52\right)$

And O _1xN-1And O _N-1x1Be respectively to have N-1 zero row vector and column vector.

J is that matrix is drawn in following providing (N-1) * (N-1) counterclaim

In equation (53), the blank space in the square bracket is represented all null matrix elements.

As can be seen, it is two N * 1 complex vector computes integer FFT that lifting matrix factor decomposed form can be used to use method described herein from equation (51).

In this embodiment, the calculating of territory conversion only needs 3N the operation that rounds up, as what will describe now.

Suppose that respectively α (*) is the number of times of real addition,

μ (*) is the number of times of real multiplication, and

γ (*) is the real number of times that rounds up.

IntFFT algorithm for described proposition can obtain:

α(IntFFT)＝6N+3α(FFT)

μ(IntFFT)＝3μ(FFT)

γ(IntFFT)＝6N

Because the IntFFT algorithm of described proposition is handled together to them, so The above results is at two pieces of data sampling.Thus, for a piece of data sampling, the number of times of described calculating is halved, and it is

α ₁(IntFFT)＝3N+1.5α(FFT)

μ ₁(IntFFT)＝1.5μ(FFT)

γ ₁(IntFFT)＝3N

α wherein ₁, μ ₁And γ ₁Be respectively number of times and the real number of operations that rounds up at the number of times of the real addition of a piece of sampling, real multiplication.

Calculate for FFT, can use the algorithm of split-radix FFT (SRFFT), according to this algorithm

α(SRFFT)＝3Nlog ₂ N-3N+4

μ(SRFFT)＝Nlog ₂ N-3N+4

As a result, we obtain:

α ₁(IntFFT)＝4.5Nlog ₂ N-1.5N+6

μ ₁(IntFFT)＝1.5Nlog ₂ N-4.5N+6

Fig. 7 shows the direct transform scrambler and the inverse transformation scrambler of the conversion degree of accuracy that is used to evaluate above-mentioned dct transform technology and above-mentioned FFT territory conversion.Described test relate to according to here introduce in March, 2003 Thailand ISO/IEC JTC 1/SC 29/WG 11 N5778 Pattaya, evaluation criteria that is proposed by MPEG-4 lossless audio coding group of describing in " Codingof Moving Pictures and Audio:Work plan for Evaluation of Integer MDCTfor FGS to Lossless Experimentation Framework " is measured the average variance (MSE) of conversion.

Particularly, following the providing of MSE of the anti-DCT of IntDCT and integer (IntIDCT)

$\mathrm{MSE}=\frac{1}{K}\underset{j=0}{\overset{K-1}{\mathrm{\&Sigma;}}}\frac{1}{N}\underset{i=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{e}_i^2---\left(54\right)$

Wherein, for IntDCT, error signal e is e _jFor IntIDCT, error signal e is e _i, as shown in fig. 1.K is the sum of the sampling block that uses in the described assessment.

Following the providing of MSE of the anti-FFT of IntFFT and integer (IntIFFT)

$\mathrm{MSE}=\frac{1}{K}\underset{j=0}{\overset{K-1}{\mathrm{\&Sigma;}}}\frac{1}{N}\underset{i=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|\right|e_i\left|\right|}^2---\left(55\right)$

Wherein, for IntFFT, error signal e is e _jFor IntIFFT, error signal e is e _i, as shown in fig. 1.|| * || the mould of expression complex values.K is the sum of the sampling block that uses in the described assessment.

For two kinds of territory conversion, in 48kHz/16 bit test group, used 450 seconds altogether with 15 different genres of music files.Table I shows described test result.

As can be seen from Table 1, the MSE that uses system and method for the present invention to produce is very little, and unlike conventional system, irrelevant with the size of processing block basically.With reference to the conversion of DCT-IV territory, when block size N being increased to nearly 4096 bits, described MSE only increases a little.The MSE of described FFT even better increases to 4096 bits for block size, demonstrates stable MSE 0.4.When according to the ability that is presented with to the performance that growth of requirement the present invention showed of longer block size, advantage of the present invention is more obvious.

N

IntDCT-IV

IntIDCT-IV

IntFFT

IntIFFT

8	0.537	0.537	0.456	0.371
					16	0.546	0.546	0.480	0.412
32	0.549	0.548	0.461	0.391
					64	0.550	0.550	0.462	0.393
128	0.551	0.551	0.461	0.391
					256	0.552	0.552	0.461	0.391
512	0.552	0.552	0.461	0.391
					1024	0.552	0.552	0.460	0.391
2048	0.552	0.552	0.461	0.391
					4096	0.553	0.552	0.461	0.391

Table I

Introduce document

Introduce following document here by reference:

H.S.Malver，“Signal Processing with Lapped Transforms”ArtechHouse，1992；

R.Geiger，T.Sporer，J.Koller，K.Brandenburg，“Audio Coding basedon Integer Transforms”AES 111 ^th Convention，New York，USA，Sept.2001；

Wang，Zhongde，“On Computing the Discrete Fourier and CosineTransforms”，IEEE Transactions on Acoustics，Speech and SignalProcessing，Vol.ASSP-33，No.4 October 1985；

I.Daubechies and W.Sweldens，″Factoring wavelet transforms intolifting steps″，Tech.Report，Bell Laboratories，Lucent Technologies，1996；

S.Oraintara，Y.J.Chen and T.Q.Nguyen，″Integer fast Fouriertransform″，IEEE Trans.Signal Processing，vol.50，no.3，Mar.2002，pp.607-618；

P.Hao and Q.Shi，″Matrix factorizations for reversible integermapping，″IEEE Trans.Signal Processing，vol.49，no.10，Oct.2001，pp.2314-2324；

G.Plonka and M.Tasche，″Invertible integer DCT algorithms″，Appl.Comput.Harmon.Anal.15：70-88，2003；

Y.H.Zeng，L.Z.Cheng，G.A.Bi，and Alex C.Kot，″Integer DCTs andfast algorithms″，IEEE Trans.Signal Processing，vol.49，no.11，Nov.2001，pp.2774-2782；

J.Wang，J.Sun and S.Yu，″1-D and 2-D transforms from integers tointegers″，in Proc.Int.Conf.Acoustics，Speech and Signal Processing，Hong Kong，2003，vol.II，pp.549-552；

″Coding of Moving Pictures and Audio：Work plan for Evaluation ofInteger MDCT for FGS to Lossless Experimentation Framework″，ISO/IEC JTC I/SC 29/WG 11 N5578，Pattaya，Thailand，Mar.2003.

Claims (13)

1, a kind ofly be used to use transforming function transformation function that digital signal is transformed from the time domain to frequency domain and the method from the frequency domain transform to the time domain, described transforming function transformation function comprises transformation matrix, described digital signal comprises a plurality of data symbols, and be divided into a plurality of, wherein each piece comprises the described data symbol of predetermined number, and described method comprises:

Utilize a conversion unit two pieces of the described digital signal of conversion usually, wherein said conversion element is corresponding to the block diagonal matrix that comprises two submatrixs, wherein each submatrix comprises described transformation matrix, described conversion element comprises a plurality of lifting levels, and wherein each lifting level comprises by the householder transformation unit and a plurality of piece processing carried out of unit to described digital signal that round up.

2, the method for claim 1, wherein, described transforming function transformation function is DCT-I transforming function transformation function, DCT-IV transforming function transformation function, DFT-I transforming function transformation function, DFT-IV transforming function transformation function, DST-I transforming function transformation function, DST-IV transforming function transformation function, DWT-I transforming function transformation function or DWT-IV transforming function transformation function.

3, method as claimed in claim 1 or 2, wherein, each promotes level and promotes matrix corresponding to one, wherein said lifting matrix is the block-tridiagonal matrix that comprises four submatrixs, wherein two reversible INTEGER MATRICES are as two described submatrixs on the diagonal angle, and described transformation matrix and zero is as two other submatrix on another diagonal line.

4, method as claimed in claim 3, wherein, each described reversible INTEGER MATRICES that promotes in the matrix is unit matrix or negative unit matrix.

5, the method for claim 1, wherein described conversion element comprises that three promote level.

6, the method for claim 1, wherein sound signal or vision signal are used as described digital signal.

7, a kind ofly be used to use transforming function transformation function that digital signal is transformed from the time domain to frequency domain and the equipment from the frequency domain transform to the time domain, described transforming function transformation function comprises transformation matrix, described digital signal comprises a plurality of data symbols and is divided into a plurality of, wherein each piece comprises the described data symbol of predetermined number, and described equipment comprises:

Converter unit, it utilizes a conversion unit two pieces of the described digital signal of conversion usually, wherein said conversion element is corresponding to the block diagonal matrix that comprises two submatrixs, and wherein each submatrix comprises described transformation matrix, and described conversion element comprises a plurality of lifting levels.

8, equipment as claimed in claim 7, wherein, described converter unit comprises and is used for the householder transformation unit that each promotes level, is used to handle described of described digital signal.

9, as described equipment in claim 7 or 8, wherein, described converter unit comprises and is used for the unit that rounds up that each promotes level, is used to handle described of described digital signal.

10, equipment as claimed in claim 7, wherein, described converter unit comprises:

Improve discrete cosine transformation apparatus, it is coupled and receives described a plurality of, and is configured to each piece territory is transformed to the MDCT coefficient;

Quantizer, it is coupled and receives each described MDCT coefficient, and in response to the reception to this MDCT coefficient, described quantizer is used for producing the MDCT coefficient that has quantized;

Bitstream encoder, it is coupled and receives the described MDCT coefficient that has quantized, and in response to the reception of the MDCT coefficient that this has been quantized, described bitstream encoder produces the bit stream of perceptual coding;

First inverse quantizer, it is coupled and receives the MDCT coefficient that has quantized, and described first inverse quantizer is used for described MDCT coefficient is returned to non-quantification state; With

First unit that rounds up, it is coupled and receives the MDCT coefficient that is recovered by described first inverse quantizer, and is used to produce round values MDCT coefficient.

11, equipment as claimed in claim 10, wherein, described converter unit also comprises:

Integer improves discrete cosine transformation apparatus, and it is coupled and receives described, and in response to described reception, is used to produce the IntMDCT coefficient;

Calculation element is used to calculate the difference between each IntMDCT coefficient and the round values MDCT coefficient, to produce each remaining MDCT coefficient; And

Entropy coder, it is coupled and receives described remaining MDCT coefficient, and in response to the reception to described remaining MDCT coefficient, is used to produce the harmless bit stream that strengthens.

12, equipment as claimed in claim 11, wherein, described converter unit also comprises:

The bit stream decoding device, it is coupled and receives the bit stream of described perceptual coding, and in response to the reception to the bit stream of described perceptual coding, is used to export decoded bit stream;

Second inverse quantizer, it is coupled and receives described decoded bit stream, and in response to the reception to described decoded bit stream, described second inverse quantizer produces the MDCT coefficient that has recovered;

Second unit that rounds up, it is coupled from second inverse quantizer and receives the described MDCT coefficient that has recovered, and the MDCT coefficient that is used for each has been recovered is rounded to round values; And

Anti-MDCT equipment, it is coupled and receives the described MDCT coefficient that has recovered, and in response to the reception to the described MDCT coefficient that has recovered, is used to produce the described perceptual coding signal of reconstruct.

13, equipment as claimed in claim 12, wherein, described converter unit comprises:

Entropy decoder, it is coupled and receives described harmless enhancing bit stream, and in response to this harmless reception that strengthens bit stream, is used to produce remaining IntMDCT coefficient;

Adding device is used for described remaining IntMDCT coefficient is produced the IntMDCT coefficient in the Calais mutually with described round values MDCT coefficient; And

Anti-IntMDCT equipment, its be coupled receive described round values MDCT coefficient and described IntMDCT coefficient and, with duplicating of a lossless coding sound signal that produces reconstruct.

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