CN102355269A - One-dimensional segment code signal rapid decoding method based on GDHT-III domain - Google Patents

Abstract

The invention discloses a one-dimensional segment code signal rapid decoding method based on a GDHT (generalized discrete Hartley transform)-III domain, belonging to the signal processing technology field. GDHT-III domain coefficients {Ak}, {Bk} and {Ck} (k is an integer from 0 to N/3-1) of signal sequences {an}, {bn} and {cn} with a length of N/3 (n is an integer from 0 to N/3-1) are converted into a GDHT-III domain coefficient {Xi} (i is an integer from 0 to N-1) of an original code signal sequence {xm} (m is an integer from 0 to N-1) of a length of N, wherein, calculation of {Xi} is divided into a multiple of 3 output index {X3k}, a multiple of 3 with a reminder 1 output index {X3k+1} and a multiple of 3 with a reminder 2 output index {X3k+2} to carry out calculation respectively, thus GDHT-III transformation times are reduced, and calculation complexity of a decoding process is reduced. Compared with the prior art, the method in the invention has the characteristics of lower complexity, better decoding real-time property, and less signal distortion.

Description

GDHT-III domain-based one-dimensional segmented coding signal fast decoding method

Technical Field

The invention relates to a signal decoding method, in particular to a one-dimensional segmented coding signal fast decoding method based on a GDHT-III domain, and belongs to the technical field of signal processing.

Background

Codec is an extremely important part of digital signal processing technology, coding refers to converting an input signal into a code that is optimized for transmission or storage, and decoding is the reverse process of coding. The codec process is typically performed by a codec device. The general signal encoding process usually includes several processes of time domain forward transform, quantization, entropy coding, and the decoding process includes inverse entropy coding, inverse quantization, and frequency domain inverse transform.

The Discrete Hartley Transform (DHT) is an important mathematical tool in digital signal processing, which can describe the relationship between the time domain and the frequency domain of a Discrete signal, and has a very important position in digital signal processing. As an extension of DHT, the Generalized Discrete Hartley Transform (GDHT) can be applied to a wider field. There are four forms of GDHT, GDHT-I (i.e., DHT), GDHT-II, GDHT-III and GDHT-IV. The inherent real mapping property of the GDHT kernel itself makes it well suited for processing real signal sequences.

Input sequence { x_mGDHT-III of N-1 is defined as

<math> <mrow> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mi>N</mi> <mi>III</mi> </msubsup> <mo>{</mo> <msub> <mi>x</mi> <mi>m</mi> </msub> <mo>}</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>x</mi> <mi>m</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mi>N</mi> </mfrac> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>0,1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> </mrow> </math>

The inverse transformation (IGDHT-III) is defined as

<math> <mrow> <msub> <mi>x</mi> <mi>m</mi> </msub> <mo>=</mo> <msubsup> <mi>IGDHT</mi> <mi>N</mi> <mi>III</mi> </msubsup> <mo>{</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>}</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>X</mi> <mi>i</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;k</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mi>N</mi> </mfrac> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>0,1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> </mrow> </math>

Where N is the sequence length and cas α + sin α in the following discussion we ignore the normalization factor 1/N in equation (1) because it is only a constant division calculation. Such as: for N2^lL is more than or equal to 2, which only needs to do simple shift operation.

GDHT-III (and IGDHT-III) has unique advantages in handling real signal compression coding as an alternative to DFT (and IDFT): firstly, the kernel function is a real function, and when the input is a real signal, only real number operation is needed, so that the calculation complexity is lower than that of DFT; second, the positive and negative transforms have the same form, so the positive and negative transforms can be realized by the same module.

In the existing coding and decoding method based on GDHT-III transformation, a signal { x needs to be transmitted_mThe length is usually relatively long, so that the signal needs to be sent by coding in segments, wherein a common case is that { x } is used_mIs equally divided into three sections { a }_n}，{b_nAnd { c }and_nI.e. a_n＝x_n，b_n＝x_n+N/3，c_n＝x_n+2N/3N is 0, 1,.., N/3-1. Firstly, first of all { a_n}，{b_nAnd { c }and_nThe corresponding transform domain coefficients { A } are obtained by GDHT-III transform respectively_k}，{B_kAnd { C }_kThen, the coefficients are quantized, entropy-coded and the like to obtain coefficients { A'_k}，{B′_kAnd { C'_kIs transmitted to the receiving end. Upon decoding, the received coefficients { A'_k}，{B′_kAnd { C'_kRespectively carrying out inverse entropy coding, inverse quantization and other processing to obtain a recovered coefficient { A }_k}，{B_kAnd { C }_kThe key question involved is how to go through { A }_k}，{B_kAnd { C }_kCalculate { X }_i(wherein { X)_iIs { x }_nCoefficient of GDHT-III of length N)? Since the real-time performance requirements of signal coding and decoding are quite high, the lower the complexity requirement, the better the quality assurance. Now thatThere is a method that firstly the input GDFT-II domain coefficient { A with the length of N/3_k}，{B_kAnd { C }_kRespectively obtaining the original time domain signals { a ] through IGDHT-III inverse transformation and time domain transformation_n}，{b_nAnd { c }and_nThen combine these three sequences in series into { x }_mAnd then calculating a sequence { x with the length of N_mCoefficient of GDHT-III { X }_i}. Therefore, the traditional method needs to calculate three IGDHT-III with the length of N/3 and one GDHT-III with the length of N, and needs higher calculation complexity, thereby influencing the decoding real-time performance to a certain extent.

Disclosure of Invention

The technical problem to be solved by the invention is to overcome the technical problems of high computational complexity and poor decoding real-time performance of the existing one-dimensional segmented coding signal decoding method based on the GDHT-III domain, and provide a one-dimensional segmented coding signal fast decoding method based on the GDHT-III domain, wherein the method has low computational complexity and good decoding real-time performance.

The invention adopts the following technical scheme:

a one-dimensional segmented coding signal fast decoding method based on GDHT-III domain, the segmented coding signal is obtained by equally dividing original signal sequence with length N into three signal sequences with length N/3, then respectively carrying out GDHT-III transformation on the three signal sequences to obtain corresponding GDHT-III domain coefficients, and finally respectively carrying out quantization and entropy coding processing on the three groups of GDHT-III domain coefficients, the fast decoding method comprises the following steps:

step 1, performing inverse entropy coding and inverse quantization processing on the segmented coding signals to obtain three groups of recovered GDHT-III domain coefficients;

step 2, setting the three groups of GDHT-III domain coefficients obtained in the step 1 as { A }_k}、{B_kAnd { C }_kK is 0, 1,.., N/3-1, and the sequence { X is calculated according to the following formula, respectively_3k}、{X_3k+1}、{X_3k+2Where k is 0, 1.., N/3-1: x_3k+1＝A_k-B_k+C_k，k＝0，1，...，N/3-1

$X_{3k}=\frac{1}{2}(Y_k+Z_k),k=\mathrm{0,1,2}\mathrm{L\; L},N/3-1,$

$X_{3k+2}=\frac{1}{2}(Y_k-Z_k),k=\mathrm{0,1,2}\mathrm{L\; L},N/3-1$

Wherein,

<math> <mrow> <msub> <mi>Y</mi> <mi>k</mi> </msub> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mo>{</mo> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> <mo>,</mo> </mrow> </math>

<math> <mrow> <msub> <mi>Z</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mo>{</mo> <mo>-</mo> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> <mo>,</mo> </mrow> </math>

in the formula,

and

respectively representing the forward and reverse GDHT-III transformations of length N/3 on the signal sequence in brackets, theta _n2N/N is a twiddle factor;

step 3, converting the sequence { X }_3k}、{X_3k+1}、{X_3k+2The elements in the sequence are sequentially connected in series to be combined to obtain a sequence (X)_i}; wherein k is 0, 1,.., N/3-1; i-0, 1, ·, N-1; sequence { X_iI.e. the GDHT-III domain coefficient of the original signal sequence of length N.

Compared with the prior art, the method has the advantages of low calculation complexity and better decoding instantaneity. The inventive method also has less signal distortion because, in general, the GDHT-III transform is followed by a quantization step, whereas the use of IGDHT-III with quantized coefficients results in signal distortion. The error is further increased by GDHT-III transformation of the distorted signal. Therefore, to reduce signal distortion, we need to minimize the number of IGDHT-III and GDHT-III. While the conventional method requires three IGDHT-III and three GDHT-III, the method of the present invention requires only two IGDHT-III and two GDHT-III. The inventive method therefore has less signal distortion.

Drawings

FIG. 1 is a schematic flow chart of a conventional method for performing segmented encoding;

FIG. 2 is a flow chart illustrating a conventional method for performing segmented decoding;

FIG. 3 is a signal flow diagram of a fast decoding method based on GDHT-III transform according to the present invention; where the numbers next to the arrowed line indicate the transmission factor (corresponding to the multiplier),an adder is shown. "deconvolution" means that the signal sequence { Z }is inverted_N/3-1-kConvert to { Z }_k}，k＝0，1，....，N/3-1。

Detailed Description

The technical scheme of the invention is explained in detail in the following with the accompanying drawings:

FIG. 1 shows the conventional block encoding procedure, first transmitting a signal { x }_mIs equally divided into three sections { a }_n}，{b_nAnd { c }and_nI.e. a_n＝x_n，b_n＝x_n+N/3，c_n＝x_n+2N/3N is 0, 1,.., N/3-1, and is paired with { a ═ a, respectively_n}，{b_nAnd { c }and_nCarry out GDHT-III transform to obtain its corresponding coefficient { A }_k}，{B_kAnd { C }_kN/3-1, and then quantizing and entropy-coding the coefficients to obtain coefficients { a'_k}，{B′_kAnd { C'_kIt is transmitted to the receiving end or stored in the medium.

FIG. 2 shows the flow of segment decoding by the conventional method, first on the received coefficients { A'_k}，{B′_kAnd { C'_kRespectively carrying out inverse entropy coding and inverse quantization processing to obtain a recovered coefficient { A }_k}，{B_kAnd { C }_kAnd obtaining the original time domain signal { a } of the coefficients through IGDHT-III_n}，{b_nAnd { c }and_nThen combine these three sequences in series into { x }_mAnd then calculating a sequence { x with the length of N_nCoefficient of GDHT-III { X }_i}. When the conventional method is used, if { x is input_mIs a real signal with a computational complexity of

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msup> <mi>M</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>6</mn> <msup> <mi>M</mi> <mi>III</mi> </msup> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>=</mo> <mi>N</mi> <msub> <mi>log</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mi>A</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>6</mn> <msup> <mi>A</mi> <mi>III</mi> </msup> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>8</mn> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>=</mo> <mn>3</mn> <mi>N</mi> <msub> <mi>log</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>-</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>+</mo> <mn>24</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>N</mi> <mo>=</mo> <mn>3</mn> <mo>&times;</mo> <msup> <mn>2</mn> <mi>l</mi> </msup> <mo>,</mo> <mi>l</mi> <mo>&GreaterEqual;</mo> <mn>2</mn> <mo>.</mo> </mrow> </math>

Wherein M is^III(N) and A^III(N) are the multiplicative and additive numbers, respectively, required to compute a real number GDHT-III of length N.

FIG. 3 shows a flow chart of an embodiment of the method of the present invention for decoding an N-point real signal, where the input is a real signal { a } of length N/3_n}，{b_nAnd { c }and_nThe GDHT-III domain coefficient of { A }_k}，{B_kAnd { C }_k}; the output is a real signal of length N x_mThe GDHT-III domain coefficient of { X }_i0, 1, N-1 is illustrated by { X ═ X_3k}，{X_3k+1And { X }_3k+2K is expressed in three parts, 0, 1.

When the method is adopted for decoding, one GDHT-III with the length of N is decomposed into three GDHT-III with the length of N/3 for calculation, namely { X is output_iThe calculation is divided into multiple output indices of 3X_3kMultiple of { 3 } and 1 output index { X }_3k+1Multiple of { and 3 } and 2 output index { X_3k+2The three parts are calculated separately.

Index portion { X_3k+1Obtained according to the following formula

<math> <mrow> <msub> <mi>X</mi> <mrow> <mn>3</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>x</mi> <mi>m</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>2</mn> <mrow> <mo>(</mo> <mn>3</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mi>N</mi> </mfrac> </mrow> </math>

<math> <mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>a</mi> <mi>n</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;n</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> </mfrac> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>b</mi> <mi>n</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;n</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> </mfrac> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>0,1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>.</mo> </mrow> </math>

<math> <mrow> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>c</mi> <mi>n</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;n</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </math>

$=A_k-B_k+C_k$

Index portion { X_3kAnd { X }_3k+1The calculation is carried out according to the following two steps:

the first step is as follows: constructing and calculating an intermediate quantity Y_kAnd Z_k，k＝0，1，...，N/3-1

Order to

Y_k＝X_3k+X_3k+2，k＝0，1，...，N/3-1

Z_k＝X_3k-X_3k+2，k＝0，1，...，N/3-1

Then Y is_kAnd Z_kObtained according to the following formula

<math> <mrow> <msub> <mi>Y</mi> <mi>k</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>x</mi> <mi>m</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>6</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mi>N</mi> </mfrac> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>x</mi> <mi>m</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>6</mn> <mi>k</mi> <mo>+</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> <mi>N</mi> </mfrac> </mrow> </math>

<math> <mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mi>m</mi> </msub> <mi>cos</mi> <mfrac> <mrow> <mn>2</mn> <mi>&pi;m</mi> </mrow> <mi>N</mi> </mfrac> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </math>

<math> <mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>{</mo> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>a</mi> </mrow> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </math>

<math> <mrow> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mo>{</mo> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>a</mi> </mrow> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> </mrow> </math>

<math> <mrow> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mo>{</mo> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mo>C</mo> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> </mrow> </math>

<math> <mrow> <msub> <mi>Z</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>x</mi> <mi>m</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>6</mn> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mi>N</mi> </mfrac> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>x</mi> <mi>m</mi> </msub> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>6</mn> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> <mi>N</mi> </mfrac> </mrow> </math>

<math> <mrow> <mo>=</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mi>m</mi> </msub> <mi>sin</mi> <mfrac> <mrow> <mn>2</mn> <mi>&pi;m</mi> </mrow> <mi>N</mi> </mfrac> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </math>

<math> <mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>{</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>a</mi> </mrow> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> <mi>cas</mi> <mfrac> <mrow> <mi>&pi;m</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </math>

<math> <mrow> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mo>{</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>a</mi> </mrow> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <mrow> <mo>(</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> </mrow> </math>

<math> <mrow> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mo>{</mo> <mo>-</mo> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mo>C</mo> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> </mrow> </math>

Wherein k is 0, 1,., N/3-1,

and

respectively representing the forward and reverse GDHT-III transformations of length N/3 on the signal sequence in brackets, theta _n2N/N is the twiddle factor.

The second step is that: by an intermediate amount Y_kAnd Z_kComputing the index portion { X_3kAnd { X }_3k+2}{X_3kAnd { X }_3k+2Can be obtained from the following formulae

$X_{3k}=\frac{1}{2}(Y_k+Z_k),$ k＝0，1，...，N/3-1

$X_{3k+2}=\frac{1}{2}(Y_k-Z_k),$

Will sequence { X_3k}、{X_3k+1}、{X_3k+2Sequentially combining elements in series to obtain a GDHT-III domain coefficient { X ] of an original signal sequence with the length of N_i}。

When the method of the invention is adopted for decoding, if { x is input_mIs a real signal with computational complexity:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msup> <mi>M</mi> <mi>P</mi> </msup> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mn>4</mn> <mi>M</mi> </mrow> <mi>III</mi> </msup> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <msub> <mi>log</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mi>A</mi> <mi>P</mi> </msup> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>4</mn> <msup> <mi>A</mi> <mi>III</mi> </msup> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>3</mn> <mi>N</mi> <mo>=</mo> <mn>2</mn> <mi>N</mi> <msub> <mi>log</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>N</mi> <mo>+</mo> <mn>16</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>N</mi> <mo>=</mo> <mn>3</mn> <mo>&times;</mo> <msup> <mn>2</mn> <mi>l</mi> </msup> <mo>,</mo> <mi>l</mi> <mo>&GreaterEqual;</mo> <mn>2</mn> <mo>.</mo> </mrow> </math>

wherein M is^III(N) and A^III(N) are the multiplicative and additive numbers, respectively, required to compute a real number GDHT-III of length N.

Table 1 below shows the comparison of computational complexity (input as real signal) when decoding is performed using the method of the present invention versus using the conventional method.

TABLE 1

As can be seen from table 1, the decoding method of the present invention is more efficient than the conventional method. For real input signals, the inventive method saves 17% to 26% of computational complexity over the conventional method when the sequence length N is increased from 12 to 192. Also, the present invention has less signal distortion because it uses fewer GDHT-III/IGDHT-III transforms.

Claims (1)

1. A one-dimensional segmented coding signal fast decoding method based on GDHT-III domain, the segmented coding signal is obtained by equally dividing original signal sequence with length N into three signal sequences with length N/3, then respectively carrying out GDHT-III transformation on the three signal sequences to obtain corresponding GDHT-III domain coefficients, and finally respectively carrying out quantization and entropy coding processing on the three groups of GDHT-III domain coefficients, the fast decoding method is characterized by comprising the following steps:

step 1, performing inverse entropy coding and inverse quantization processing on the segmented coding signals to obtain three groups of recovered GDHT-III domain coefficients;

step 2, setting the three groups of GDHT-III domain coefficients obtained in the step 1 as { A }_k}、{B_kAnd { C }_kK is 0, 1,.., N/3-1, and the sequence { X is calculated according to the following formula, respectively_3k}、{X_3k+1}、{X_3k+2Where k is 0, 1.., N/3-1: x_3k+1＝A_k-B_k+C_k，k＝0，1，...，N/3-1

$X_{3k}=\frac{1}{2}(Y_k+Z_k),k=\mathrm{0,1,2}\mathrm{L\; L},N/3-1,$

$X_{3k+2}=\frac{1}{2}(Y_k-Z_k),k=\mathrm{0,1,2}\mathrm{L\; L},N/3-1$

Wherein,

<math> <mrow> <msub> <mi>Y</mi> <mi>k</mi> </msub> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mo>{</mo> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> <mo>,</mo> </mrow> </math>

<math> <mrow> <msub> <mi>Z</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>GDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mo>{</mo> <mo>-</mo> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>+</mo> <msqrt> <mn>3</mn> </msqrt> <msubsup> <mi>IGDHT</mi> <mrow> <mi>N</mi> <mo>/</mo> <mn>3</mn> </mrow> <mi>III</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>&theta;</mi> <mi>n</mi> </msub> <mo>}</mo> <mo>,</mo> </mrow> </math>

in the formula,

and

respectively representing the forward and reverse GDHT-III transformations of length N/3 on the signal sequence in brackets, theta_n2N/N is a twiddle factor;

step 3, converting the sequence { X }_3k}、{X_3k+1}、{X_3k+2The elements in the sequence are sequentially connected in series to be combined to obtain a sequence (X)_i}; wherein k is 0, 1,.., N/3-1; i-0, 1, ·, N-1; sequence { X_iI.e. the GDHT-III domain coefficient of the original signal sequence of length N.

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