CN102355269B - 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, thusGDHT-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

A kind of one dimension segment encoding signal fast decoding method based on the GDHT-III territory

Technical field

The present invention relates to a kind of signal decoding method, relate in particular to a kind of one dimension segment encoding signal fast decoding method based on the GDHT-III territory, belong to the signal processing technology field.

Background technology

Encoding and decoding are extremely important parts in the Digital Signal Processing, and coding refers to an input signal is converted to code, and this code is being beneficial to transmission or storing of optimised mistake, and decoding then is the reverse procedure of coding.Encoding-decoding process is finished by coding and decoding device usually.Common signal cataloged procedure generally includes time domain direct transform, quantification, entropy this plurality of processes of encoding, and decode procedure comprises anti-entropy coding, inverse quantization and frequency domain inverse conversion.

Discrete Hartley transform (Discrete Hartley Transform:DHT) is a kind of important mathematical tool in the Digital Signal Processing, and it can describe the relation of the time-domain and frequency-domain of discrete signal, and important status is arranged in Digital Signal Processing.As the expansion of DHT, the discrete Hartley transform of broad sense (Generalized Discrete Hartley Transform:GDHT) can be applied to field more widely.GDHT has four kinds of forms, is respectively that GDHT-I(is DHT), GDHT-II, GDHT-III and GDHT-IV.The real number Properties of Some Mapping that GDHT kernel function itself is intrinsic makes it be very suitable for handling the real signal sequence.

List entries { x _m, m=0,1 ..., the GDHT-III of N – 1 is defined as

$X_i=\mathrm{GDH}{T}_N^{\mathrm{III}}\left\{x_m\right\}=\frac{1}{N}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{x}_m\mathrm{cas}\frac{\mathrm{\πm}(2i+1)}{N},i=\mathrm{0,1},...,N-1,$

Its inverse transformation (IGDHT-III) is defined as

$x_m=\mathrm{IGDH}{T}_N^{\mathrm{III}}\left\{X_i\right\}=\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}{X}_i\mathrm{cas}\frac{\mathrm{\πk}(2m+1)}{N},m=\mathrm{0,1},...,N-1,$

Wherein N is sequence length and cas α=cos α+sin α. we ignore the normalization factor 1/N in the formula (1) in the following discussion, because it is a constant division calculation.Such as: for N=2 ^l, l 〉=2, its needs are done simple shifting function.

GDHT-III(and IGDHT-III) as DFT(and IDFT) a kind of the replacement at the compression coding and decoding of handling real signal then have its special advantages: the first, its kernel function is real function, when being input as real signal, only need carry out real arithmetic, therefore have lower computation complexity than DFT; The second, its positive and negative conversion has identical form, therefore can realize positive and negative conversion with same module.

In existing decoding method based on the GDHT-III conversion, need the signal { x that sends _mLength is long usually, sends so need carry out segment encoding to signal, wherein a kind of common situation is with { x _mBe divided into three sections { a _n, { b _nAnd { c _n, i.e. a _n=x _n, b _n=x _N+N/3, c _n=x _N+2N/3, n=0,1 ..., N/3 – 1.At first with { a _n, { b _nAnd { c _nConversion obtains its corresponding coefficient in transform domain { A through GDHT-III respectively _k, { B _kAnd { C _k, then to these coefficients quantize, obtain after the processing such as entropy coding coefficient A ' _k, B ' _kAnd C ' _kBe sent to receiving terminal.In when decoding, at first to the coefficient that receives A ' _k, B ' _kAnd C ' _kCarry out the coefficient { A that processing such as anti-entropy coding and inverse quantization are restored respectively _k, { B _kAnd { C _k, the key issue that wherein relates to is how to pass through { A _k, { B _kAnd { C _kCalculate { X _i({ X wherein _iBe { x _nLength be the coefficient of the GDHT-III of N)? because the encoding and decoding of signal are quite high to the requirement of real-time, so under the situation of ensuring the quality of products, require complexity more low more good.Existing method is to be the GDFT-II domain coefficient { A of N/3 with the length of importing earlier _k, { B _kAnd { C _kGain time domain by the IGDHT-III contravariant respectively and obtain original time-domain signal { a _n, { b _nAnd { c _n, then these three sequence tandem compounds are become { x _m, computational length is the sequence { x of N again _mThe coefficient { X of GDHT-III _i.Can know that thus the IGDHT-III that it is N/3 that traditional method need be calculated three length and the GDHT-III that length is N need higher computation complexity, thereby influence the real-time of decoding to a certain extent.

Summary of the invention

Technical problem to be solved by this invention is to overcome the technical problem of the existing existing computation complexity height of one dimension segment encoding signal decoding method based on the GDHT-III territory, decoding real-time difference, a kind of one dimension segment encoding signal fast decoding method based on the GDHT-III territory is provided, this method has lower computation complexity, and the decoding real-time is better.

The present invention is by the following technical solutions:

A kind of one dimension segment encoding signal fast decoding method based on the GDHT-III territory, described segment encoding signal is by being that the original signal sequence of N is divided into the burst that three segment length are N/3 with length, respectively this three segment signals sequence is carried out the GDHT-III conversion then and obtain its corresponding GDHT-III domain coefficient, at last to these three groups of GDHT-III domain coefficients quantize respectively, entropy coding handles and obtains, described fast decoding method may further comprise the steps:

Step 1, to the segment encoding signal carry out anti-entropy coding, inverse quantization is handled three groups of GDHT-III domain coefficients that are restored;

Step 2, establish three groups of GDHT-III domain coefficients that step 1 obtains and be respectively { A _k, { B _kAnd { C _k, k=0,1 ...,

N/3 – 1 is respectively according to the following formula sequence of calculation { X _3k, { X _3k+1, { X _3k+2, k=0 wherein, 1 ..., N/3 – 1:

X _3k+1=A _k-B _k+C _k，k=0,1,…,N/3–1

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

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

Wherein,

$Y_k=\mathrm{GDH}{T}_{N/3}^{\mathrm{III}}\{\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(2A_k+B_k-C_k)\cos {\mathrm{\θ}}_n+\sqrt{3}\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(B_k+C_k)\sin {\mathrm{\θ}}_n\},$

$Z_{N/3-1-k}=\mathrm{GDH}{T}_{N/3}^{\mathrm{III}}\{-\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(2A_k+B_k-C_k)\sin {\mathrm{\θ}}_n+\sqrt{3}\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(B_k+C_k)\cos {\mathrm{\θ}}_n\},$

In the formula,

With

Represent that respectively be forward and the oppositely GDHT-III conversion of N/3 to the burst in the bracket as length, θ _n=2 π n/N are twiddle factors;

Step 3, with sequence { X _3k, { X _3k+1, { X _3k+2In element successively tandem compound obtain sequence { X _i; K=0 wherein, 1 ..., N/3 – 1; I=0,1 ..., N – 1; Sequence { X _iBe the GDHT-III domain coefficient that length is the original signal sequence of N.

Compared to existing technology, the computation complexity that the inventive method has is lower, and the real-time of decoding is better.The inventive method also has distorted signals still less, and this is because as a rule, the step that and then can quantize after the signal process GDHT-III conversion, and utilize IGDHT-III can cause the distortion of signal with the coefficient after quantizing.Signal after the distortion carries out the GDHT-III conversion again will make error further strengthen.Therefore, in order to reduce the distortion of signal, our will try one's best number of less IGDHT-III and GDHT-III.Traditional method need be carried out three IGDHT-III and three GDHT-III, and the inventive method only needs twice IGDHT-III and twice GDHT-III.Therefore the inventive method has distorted signals still less.

Description of drawings

Fig. 1 carries out the schematic flow sheet of segment encoding for existing method;

Fig. 2 carries out the schematic flow sheet of segmentation decoding for existing method;

Fig. 3 is the signal flow graph of the fast decoding method based on the GDHT-III conversion of the present invention; Wherein with the numeral transmission factor (being equivalent to multiplier) by the line segment of arrow, " ⊕ " represents adder." anti-pleat " expression is with burst { Z _N/3-1-kConvert { Z to _k, k=0,1 ...., N/3-1.

Embodiment

Below in conjunction with accompanying drawing technical scheme of the present invention is elaborated:

Fig. 1 has shown the flow process of traditional segment encoding, the signal { x that at first will send _mBe divided into three sections { a _n, { b _nAnd { c _n, i.e. a _n=x _n, b _n=x _N+N/3, c _n=x _N+2N/3, n=0,1 ..., N/3 – 1, and respectively to { a _n, { b _nAnd { c _nCarry out the GDHT-III conversion and obtain its corresponding coefficient { A _k, { B _kAnd { C _k, k=0,1 ..., N/3 – 1, then to these coefficients quantize, entropy coding obtains coefficient after handling A ' _k, B ' _kAnd C ' _k, it is sent to receiving terminal or is stored in the medium.

Fig. 2 has shown that conventional method carries out the flow process of segmentation decoding, at first to the coefficient that receives A ' _k, B ' _kAnd C ' _kCarry out the coefficient { A that anti-entropy coding and inverse quantization processing are restored respectively _k, { B _kAnd { C _k, and these coefficients are obtained original time-domain signal { a by IGDHT-III respectively _n, { b _nAnd { c _n, then these three sequence tandem compounds are become { x _m, computational length is the sequence { x of N again _nThe coefficient { X of GDHT-III _i.When adopting conventional method, if input { x _mBe real signal, its computation complexity is

$\left\{\begin{array}{c}{M}^T\left(N\right)=6M^{\mathrm{III}}(N/3)+4N/3=\mathrm{Nlo}{g}_2(N/3)+N/3\\ A^T\left(N\right)=6A^{\mathrm{III}}(N/3)+8N/3=3\mathrm{Nlo}{g}_2(N/3)-N/3+24\end{array},N=3\×2^l,l\≥2.\right.$

M wherein ^III(N) and A ^III(N) be respectively that computational length is the needed multiplication number of real number GDHT-III and the addition number of N.

Fig. 3 has provided the specific implementation flow graph that carries out the decoding of N point real number signal with the inventive method, and wherein input is that length is the real number signal { a of N/3 _n, { b _nAnd { c _nGDHT-III domain coefficient { A _k, { B _kAnd { C _k; Output is that length is the real number signal { x of N _mGDHT-III domain coefficient { X _i, i=0,1 ..., pass through { X among N – 1 figure _3k, { X _3k+1And { X _3k+2K=0,1 ..., 1, three part of N/3 – is expressed.

When adopting the inventive method to decode, the length GDHT-III that is N the GDHT-III that to be decomposed into three length be N/3 is calculated, be about to output { X _iCalculating be divided into 3 multiple output index { X _3k, 3 multiple is surplused 1 output index { X _3k+1And 3 multiple surplus 2 output index { X _3k+2Three parts calculate respectively.

Index part { X _3k+1Obtain according to following formula

$X_{3k+1}=\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{x}_m\mathrm{cas}\frac{\mathrm{\πm}(2(3k+1)+1)}{N}$

$=\underset{n=0}{\overset{N/3-1}{\mathrm{\Σ}}}{a}_n\mathrm{cas}\frac{\mathrm{\πn}(2k+1)}{N/3}-\underset{n=0}{\overset{N/3-1}{\mathrm{\Σ}}}{b}_n\mathrm{cas}\frac{\mathrm{\πn}(2k+1)}{N/3},k=\mathrm{0,1},...,N/3-1.$

$+\underset{n=0}{\overset{N/3-1}{\mathrm{\Σ}}}{c}_n\mathrm{cas}\frac{\mathrm{\πn}(2k+1)}{N/3}$

$=A_k-B_k+C_k$

Index part { X _3kAnd { X _3k+1Calculate according to following two steps:

The first step: structure also calculates intermediate quantity Y _kAnd Z _k, k=0,1 ..., N/3 – 1 order

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

Y then _kAnd Z _kObtain according to following formula

$Y_k=\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{x}_m\mathrm{cas}\frac{\mathrm{\πm}(6k+1)}{N}+\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{x}_m\mathrm{cas}\frac{\mathrm{\πm}(6k+5)}{n}$

$=\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}2x_{\mathrm{<figure-callout\; id="2"\; label="m\; cos"\; filenames="110727095547.png"\; state="\{\{state\}\}">m</figure-callout>}}\cos \frac{2\mathrm{\&pi;m}}{N}\mathrm{cas}\frac{\mathrm{\&pi;m}(2k+1)}{N/3}$

$=\underset{m=0}{\overset{N/3-1}{\mathrm{\&Sigma;}}}\{(2a_n+b_n-c_n)\cos {\mathrm{\&theta;}}_n+\sqrt{3}(b_n+c_n)\sin {\mathrm{\&theta;}}_n\}\mathrm{cas}\frac{\mathrm{\&pi;m}(2k+1)}{N/3}$

$=\mathrm{GDH}{T}_{N/3}^{\mathrm{III}}\{(2a_n+b_n-c_n)\cos {\mathrm{\&theta;}}_n+\sqrt{3}(b_n+c_n)\sin {\mathrm{\&theta;}}_n\}$

$={\mathrm{GDHT}}_{N/3}^{\mathrm{III}}\{\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(2A_k+B_k-C_k)\cos {\mathrm{\&theta;}}_n+\sqrt{3}\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(B_k+C_k)\sin {\mathrm{\&theta;}}_n\}$

$Z_{N/3-1-k}=\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{x}_m\mathrm{cas}\frac{\mathrm{\&pi;m}(6(N/3-1-k)+1)}{N}-\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{x}_m\mathrm{cas}\frac{\mathrm{\&pi;m}(6(N/3-1-k)+5)}{N}$

$=-\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}2x_m\sin \frac{2\mathrm{\&pi;m}}{N}\mathrm{cas}\frac{\mathrm{\&pi;m}(2k+1)}{N/3}$

$=\underset{m=0}{\overset{N/3-1}{\mathrm{\&Sigma;}}}\{-(2a_n+b_n-c_n)\sin {\mathrm{\&theta;}}_n+\sqrt{3}(b_n+c_n)\cos {\mathrm{\&theta;}}_n\}\mathrm{cas}\frac{\mathrm{\&pi;m}(2k+1)}{N/3}$

$=\mathrm{GDH}{T}_{N/3}^{\mathrm{III}}\{-(2a_n+b_n-c_n)\sin {\mathrm{\&theta;}}_n+\sqrt{3}(b_n+c_n)\cos {\mathrm{\&theta;}}_n\}$

$={\mathrm{GDHT}}_{N/3}^{\mathrm{III}}\{-\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(2A_k+B_k-C_k)\sin {\mathrm{\&theta;}}_n+\sqrt{3}\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(B_k+C_k)\cos {\mathrm{\&theta;}}_n\}$

K=0 wherein, 1 ..., N/3 – 1,

With

Represent that respectively be forward and the oppositely GDHT-III conversion of N/3 to the burst in the bracket as length, θ _n=2 π n/N are twiddle factors.

Second step: by intermediate quantity Y _kAnd Z _k, computation index part { X _3kAnd { X _3k+2}

{ X _3kAnd { X _3k+2Can be obtained by following formula respectively

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

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

With sequence { X _3k, { X _3k+1, { X _3k+2In element successively tandem compound can obtain the GDHT-III domain coefficient { X that length is the original signal sequence of N _i.

When adopting the inventive method decoding, if input { x _mBe real signal, its computation complexity is:

$\left\{\begin{array}{c}{M}^P\left(N\right)=4M^{\mathrm{III}}(N/3)+4N/3=(2N/3)\mathrm{lo}{g}_2(N/3)+2N/3\\ A^P\left(N\right)=4A^{\mathrm{III}}(N/3)+3N=2\mathrm{Nlo}{g}_2(N/3)+N+16\end{array},N=3\&times;2^l,l\&GreaterEqual;2.\right.$

M wherein ^III(N) and A ^III(N) be respectively that computational length is the needed multiplication number of real number GDHT-III and the addition number of N.

Following table 1 has shown the computation complexity contrast (being input as real number signal) when adopting the inventive method and adopting the conventional method decoding.

Table 1

As can be seen from Table 1, coding/decoding method of the present invention is more effective than conventional method.For the real number input signal, when sequence length N was increased to 192 from 12, the inventive method had been saved 17% to 26% computation complexity than conventional method.Simultaneously, because the present invention has used the GDHT-III/IGDHT-III conversion of less number of times, therefore has distorted signals still less.

Claims (1)

1. one dimension segment encoding signal fast decoding method based on the GDHT-III territory, described segment encoding signal is by being that the original signal sequence of N is divided into the burst that three segment length are N/3 with length, respectively this three segment signals sequence is carried out the GDHT-III conversion then and obtain its corresponding GDHT-III domain coefficient, at last these three groups of GDHT-III domain coefficients are quantized respectively, the entropy coding is handled and is obtained, it is characterized in that, described fast decoding method may further comprise the steps: step 1, the segment encoding signal is carried out anti-entropy coding, inverse quantization is handled, three groups of GDHT-III domain coefficients that are restored;

Step 2, establish three groups of GDHT-III domain coefficients that step 1 obtains and be respectively { A _k, { B _kAnd { C _k, k=0,1 ..., N/3 – 1 is respectively according to the following formula sequence of calculation { X _3k, { X _3k+1, { X _3k+2, k=0 wherein, 1 ..., N/3 – 1:X _3k+1=A _k-B _k+ C _k, k=0,1 ..., N/3 – 1

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

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

Wherein, Z _kBy with following Z _N/3-1-kAnti-pleat is converted to,

$Y_k=\mathrm{GDH}{T}_{N/3}^{\mathrm{III}}\{\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(2A_k+B_k-C_k)\cos {\mathrm{\&theta;}}_n+\sqrt{3}\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(B_k+C_k)\sin {\mathrm{\&theta;}}_n\},$

$Z_{N/3-1-k}=\mathrm{GDH}{T}_{N/3}^{\mathrm{III}}\{-\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(2A_k+B_k-C_k)\sin {\mathrm{\&theta;}}_n+\sqrt{3}\mathrm{IGDH}{T}_{N/3}^{\mathrm{III}}(B_k+C_k)\cos {\mathrm{\&theta;}}_n\},$

In the formula,

With

Represent that respectively be forward and the oppositely GDHT-III conversion of N/3 to the burst in the bracket as length, θ _n=2 π n/N are twiddle factors;

Step 3, with sequence { X _3k, { X _3k+1, { X _3k+2In element successively tandem compound obtain sequence { X _i; K=0 wherein, 1 ..., N/3 – 1; I=0,1 ..., N – 1; Sequence { X _iBe the GDHT-III domain coefficient that length is the original signal sequence of N.

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