CN105608052A - Polyphase decomposition based variable point number fast Fourier transform method for GHz high-speed sampling signal - Google Patents

Abstract

The invention proposes a polyphase decomposition based variable point number fast Fourier transform (FFT) method for a GHz high-speed sampling signal. A conventional FFT processing method is decomposed and the FFT processing of the high-speed sampling signal is decomposed into the processing of a plurality of low-speed signals through a time domain polyphase decomposition technology, so that a possibility is provided for the FFT processing of the high-speed sampling signal; and after the conventional FFT processing method is decomposed into the processing of the low-speed signals in the polyphase manner, low-speed processing results are subjected to weighted synthesis to obtain a final high-speed sampling signal FFT processing result. According to the method, a new polyphase twiddle factor is established, so that the final FFT result is obtained through simple pipelining multiplication and summation operations.

Description

The variable Fast Fourier Transform (FFT) method of counting of GHz high-speed sampling signal based on heterogeneous decomposition

Technical field

The present invention relates to signal process field, particularly a kind of high-speed sampling signal is variable counts in quick FuLeaf transformation method.

Background technology

Fast Fourier Transform (FFT) (FFT) technology of high-speed sampling signal is the pass of broadband high-speed sampled signal processingOne of key technology. When the data rate of signal reaches GHz when above, traditional FFT method does not meetThe requirement of hardware process speed. Therefore, the FFT technology of high-speed sampling signal is domestic and international signal processing alwaysA focus direction. Researcher has proposed some FFT technology for high-speed sampling signal both at home and abroad,Current the most frequently used be the high-speed sampling signal based on two dimensional discrete Fourier transform of RFEL company reportDFT technology, its general principle is:

The length of hypothetical sequence x (n) is L, and L be 2 naturally power for several times, and its DFT is X (k), so

$X\left(k\right)=\underset{l=0}{\overset{L-1}{\Σ}}x\left(n\right)W_L^{nk},k=0,1,2,...,L-1$

Suppose L=M × N, so x (n) is arranged in to the matrix of the capable N row of M, ordern＝Mn₁+n₀k＝Lk₁+k₀, wherein n₁＝0，1，2，…，N-1，n₀＝0，1，2，…，M-1，k₀＝0，1，2，…，N-1，k₁＝0，1，2，…，M-1。

By n, k brings the expression formula of X (k) into, after arrangement, can obtain

$\begin{array}{c}X\left(k_1,k_0\right)=DFT\left(x\left({\mathrm{Mn}}_1+n_0\right)\right)\\ =DFT\left(x\left(n_1,n_0\right)\right)\\ =\underset{n=0}{\overset{L-1}{\mathrm{\Σ}}}x\left(n_1,n_0\right)W_N^{\left({\mathrm{Mn}}_1+n_0\right)\left({\mathrm{Nk}}_1+k_0\right)}\\ =\underset{n_0=0}{\overset{M-1}{\mathrm{\Σ}}}\left\{\[\underset{n_1=0}{\overset{N-1}{\mathrm{\Σ}}}x\left(n_1,n_0\right)W_L^{n_1{k}_0}\]W_N^{n_0{k}_0)}\right\}{W}_M^{n_0{k}_1}\\ =\underset{n_0=0}{\overset{M-1}{\mathrm{\Σ}}}\left\{X_1\left(k_0,n_0\right)W_N^{n_0{k}_0)}\right\}{W}_M^{n_0{k}_1}\end{array}$

As can be seen from the above equation, in braces, be the DFT that N is ordered, M altogether, outermost is M pointDFT. Therefore, above-mentioned quick FFT method is a two-dimentional DFT conversion process, the concrete reality of the methodExisting step is:

S1, L point data are resolved into the matrix of the capable N of M row;

S2, to all row of matrix do respectively N point DFT process;

S3, the DFT operation result of S2 is multiplied by twiddle factor;

S4, the product calculation result of S2 is done to the parallel DFT processing that M orders obtain final FFT operation result.

The shortcoming of the existing high-speed sampling FFT technology based on two-dimentional DFT is following two aspects:

(1) this Technology Need carries out twice DFT processing, and not only operand is large, and technical sophistication causes realizingDifficulty is large, and it is very large to take resource;

(2) after this FFT treatment technology is realized on hardware platform, FFT counts and can not arbitrarily change,In the time changing parameter M, will cause output interface number not mate with subsequent module, therefore, this FFT placeReason technology is in the time of practical application, and flexibility is very poor.

Summary of the invention

For solving above-mentioned the deficiencies in the prior art, the present invention proposes a kind of GHz based on heterogeneous decomposition and adopts at a high speedThe variable Fast Fourier Transform (FFT) method of counting of sample signal.

Technical scheme of the present invention is achieved in that

The variable Fast Fourier Transform (FFT) method of counting of GHz high-speed sampling signal based on heterogeneous decomposition, vacationIf the length of sequence x (n) is L, and L be 2 naturally power for several times, the L point DFT of x (n) is transformed to so:

$X\left(k\right)=\underset{l=0}{\overset{L-1}{\Σ}}x\left(n\right)W_L^{nk},k=0,1,2,...,L-1$

Make L=4M, above formula can be expressed as again:

$\begin{array}{c}X\left(k\right)=\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{3}{\mathrm{\Σ}}}x\left(4n+i\right)W_N^{\left(4n+i\right)k}\\ =\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{3}{\mathrm{\Σ}}}x\left(4n+i\right)W_M^{nk}{W}_N^{ik}\\ =\underset{i=0}{\overset{3}{\mathrm{\Σ}}}\left\{\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}x\left(4n+i\right)W_M^{nk}\right\}{W}_N^{ik}\\ =\underset{i=0}{\overset{3}{\mathrm{\Σ}}}\left\{X_i\left(k\right)\right\}{W}_N^{ik}\end{array}$

Wherein:

$X_i\left(k\right)=\underset{n=0}{\overset{M-1}{\Σ}}x(4n+i)W_M^{nk},i=0,1,2,3.$

(1) in the time of 0≤k≤M-1

$X\left(k\right)=X_0\left(k\right)+X_1\left(k\right)W_N^k+X_2\left(k\right)W_N^{2k}+X_3\left(k\right)W_N^{3k}$

(2) in the time of M≤k≤2M-1

$X\left(k\right)=X_0\left(k\right)-i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}+i\·X_3\left(k\right)W_N^{3k}$

(3) in the time of 2M≤k≤3M-1

$X\left(k\right)=X_0\left(k\right)-i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}+i\·X_3\left(k\right)W_N^{3k}$

(4) in the time of 3M≤k≤L-1

$X\left(k\right)=X_0\left(k\right)+i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}-i\·X_3\left(k\right)W_N^{3k}.$

Alternatively, the above-mentioned variable Fast Fourier Transform (FFT) of counting of GHz high-speed sampling signal based on heterogeneous decompositionMethod, comprises the following steps:

The input signal x (n) that step (1) is first L by length carries out heterogeneous 4 tunnels that are decomposed into;

Step (2), carries out M point FFT to each road signal and processes;

Step (3), the operation result that step (2) is obtained is multiplied by twiddle factor;

Step (4), the operation result that step (3) is obtained carries out real imaginary part exchange and sign conversion;

Step (5), obtains last FFT Output rusults by summation operation.

The invention has the beneficial effects as follows:

(1), by heterogeneous decomposition technique, change the FFT conversion of high-speed sampling signal into low speed signal locateReason, the FFT that realizes high-speed sampling signal on FPGA hardware platform processes;

(2) by effective heterogeneous decomposition technique and pipelining multiplier computing, saved hardware resource occupancy;

(3) parameter of counting by adjusting a FFT, realizes flexible that high-speed sampling signal FFT countsVariable, to have improved high-speed sampling FFT technology flexibility.

Brief description of the drawings

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, below will be to implementingIn example or description of the Prior Art, the accompanying drawing of required use is briefly described, and apparently, the following describesIn accompanying drawing be only some embodiments of the present invention, for those of ordinary skill in the art, do not payingGo out under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing.

Fig. 1 is the variable Fast Fourier Transform (FFT) of counting of GHz high-speed sampling signal that the present invention is based on heterogeneous decompositionThe flow chart of method.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clearlyChu, intactly description, obviously, described embodiment is only the present invention's part embodiment, instead ofWhole embodiment. Based on the embodiment in the present invention, those of ordinary skill in the art are not making creationThe every other embodiment obtaining under property work prerequisite, belongs to the scope of protection of the invention.

The existing high-speed sampling FFT Technology Need based on two-dimentional DFT carries out twice DFT processing, not onlyOperand is large, and it is large that technical sophistication causes realizing difficulty, and it is very large to take resource; This FFT treatment technologyAfter realizing on hardware platform, FFT counts and can not arbitrarily change, and in the time changing parameter M, will cause defeatedOutgoing interface number does not mate with subsequent module, and flexibility is very poor.

The present invention decomposes by the FFT processing method to traditional, by the heterogeneous decomposition technique of time domain by heightThe processing that the FFT of speed sampled signal resolves into multi-path low speed rate signal, for the FFT of high-speed sampling signal processesPossibility is provided; After the heterogeneous traditional FFT processing method processing that is decomposed into multi-path low speed signal, then will be manyRoad low-speed processing result is weighted synthetic, obtains last high-speed sampling signal FFT result. ThisBright by building new heterogeneous twiddle factor, obtain by simple pipelining multiplier and summation operationAfter FFT result.

The variable Fast Fourier Transform (FFT) of counting of GHz high-speed sampling signal based on heterogeneous decomposition that the present invention proposesThe general principle of method is:

The length of hypothetical sequence x (n) is L, and L be 2 naturally power, so the L point DFT of x (n) for several timesBe transformed to:

$X\left(k\right)=\underset{l=0}{\overset{L-1}{\Σ}}x\left(n\right)W_L^{nk},k=0,1,2,...,L-1$

Make L=4M, above formula can be expressed as again:

$\begin{array}{c}X\left(k\right)=\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{3}{\mathrm{\Σ}}}x\left(4n+i\right)W_N^{\left(4n+i\right)k}\\ =\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{3}{\mathrm{\Σ}}}x\left(4n+i\right)W_M^{nk}{W}_N^{ik}\\ =\underset{i=0}{\overset{3}{\mathrm{\Σ}}}\left\{\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}x\left(4n+i\right)W_M^{nk}\right\}{W}_N^{ik}\\ =\underset{i=0}{\overset{3}{\mathrm{\Σ}}}\left\{X_i\left(k\right)\right\}{W}_N^{ik}\end{array}$

Wherein:

$X_i\left(k\right)=\underset{n=0}{\overset{M-1}{\Σ}}x(4n+i)W_M^{nk},i=0,1,2,3.$

(1) in the time of 0≤k≤M-1

$X\left(k\right)=X_0\left(k\right)+X_1\left(k\right)W_N^k+X_2\left(k\right)W_N^{2k}+X_3\left(k\right)W_N^{3k}$

(2) in the time of M≤k≤2M-1

$X\left(k\right)=X_0\left(k\right)-i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}+i\·X_3\left(k\right)W_N^{3k}$

(3) in the time of 2M≤k≤3M-1

$X\left(k\right)=X_0\left(k\right)-i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}+i\·X_3\left(k\right)W_N^{3k}$

(4) in the time of 3M≤k≤L-1

$X\left(k\right)=X_0\left(k\right)+i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}-i\·X_3\left(k\right)W_N^{3k}$

The specific implementation step of the inventive method as shown in Figure 1, comprising:

The input signal x (n) that step (1) is first L by length carries out heterogeneous 4 tunnels that are decomposed into;

Step (2), carries out M point FFT to each road signal and processes;

Step (3), the operation result that step (2) is obtained is multiplied by twiddle factor;

Step (4), the operation result that step (3) is obtained carries out real imaginary part exchange and sign conversion;

Step (5), obtains last FFT Output rusults by summation operation.

The present invention proposes a kind of variable fast Fourier of counting of GHz high-speed sampling signal based on heterogeneous decompositionTransform method, the method structural framing is simple, is easy to realize on hardware platform.

High speed FFT reconstructing method of the present invention only need to carry out simply multichannel result and twiddle factorPipelining multiplier and summation are processed, and have significantly reduced the complexity and the resources occupation rate that realize, than existingTwo-dimensional FFT techniques save half resource.

Method of the present invention only need to be adjusted a parameter just can realize variable that FFT counts, and flexibility is high.

The foregoing is only preferred embodiment of the present invention, in order to limit the present invention, not all at thisWithin bright spirit and principle, any amendment of doing, be equal to replacement, improvement etc., all should be included in thisWithin bright protection domain.

Claims (2)

1. the variable Fast Fourier Transform (FFT) method of counting of the GHz high-speed sampling signal based on heterogeneous decomposition,It is characterized in that, the length of hypothetical sequence x (n) is L, and L be 2 naturally power, the so L of x (n) for several timesPoint DFT is transformed to:

$X\left(k\right)=\underset{l=0}{\overset{L-1}{\Σ}}x\left(n\right)W_L^{nk},k=0,1,2,...,L-1$

Make L=4M, above formula can be expressed as again:

$\begin{array}{c}X\left(k\right)=\underset{n=0}{\overset{M-1}{\Σ}}\underset{i=0}{\overset{3}{\Σ}}x\left(4n+i\right)W_N^{\left(4n+i\right)k}\\ =\underset{n=0}{\overset{M-1}{\Σ}}\underset{i=0}{\overset{3}{\Σ}}x\left(4n+i\right)W_M^{nk}{W}_N^{ik}\\ =\underset{i=0}{\overset{3}{\Σ}}\left\{\underset{n=0}{\overset{M-1}{\Σ}}x\left(4n+i\right)W_M^{nk}\right\}{W}_N^{ik}\\ =\underset{i=0}{\overset{3}{\Σ}}\left\{X_i\left(k\right)\right\}{W}_N^{ik}\end{array}$

Wherein:

$X_i\left(k\right)=\underset{n=0}{\overset{M-1}{\Σ}}x(4n+i)W_M^{nk},i=0,1,2,3;$

(1) in the time of 0≤k≤M-1

$X\left(k\right)=X_0\left(k\right)+X_1\left(k\right)W_N^k+X_2\left(k\right)W_N^{2k}+X_3\left(k\right)W_N^{3k}$

(2) in the time of M≤k≤2M-1

$X\left(k\right)=X_0\left(k\right)-i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}+i\·X_3\left(k\right)W_N^{3k}$

(3) in the time of 2M≤k≤3M-1

$X\left(k\right)=X_0\left(k\right)-i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}+i\·X_3\left(k\right)W_N^{3k}$

(4) in the time of 3M≤k≤L-1

$X\left(k\right)=X_0\left(k\right)+i\·X_1\left(k\right)W_N^k-X_2\left(k\right)W_N^{2k}-i\·X_3\left(k\right)W_N^{3k}.$

2. variable quick Fu that counts of the GHz high-speed sampling signal based on heterogeneous decomposition as claimed in claim 1In leaf transformation method, it is characterized in that, specifically comprise the following steps:

The input signal x (n) that step (1) is first L by length carries out heterogeneous 4 tunnels that are decomposed into;

Step (2), carries out M point FFT to each road signal and processes;

Step (3), the operation result that step (2) is obtained is multiplied by twiddle factor;

Step (4), the operation result that step (3) is obtained carries out real imaginary part exchange and sign conversion;

Step (5), obtains last FFT Output rusults by summation operation.