This method is easy to implement related algorithms on FPGA, which is simpler than directly using multiplication. However, the more the number of related points, the more the amount of calculation is relatively less than the direct solution.
The simulation program is as follows:
%step:
%(1) x, y complement M at the high position (data length) zeros
%(2) Find 2M point FFT, X(K), Y(K)
%(3) Product, Rxy(K)=X(K)*Y'(K) Note: Y(K) takes conjugate
%(4) Find 2M points IFFT, rxy= IFFT(Rxy(K))
Clc;close all;clear all;
X1=load('D:My DocumentsMATLABdens_flow_ejieRF1.txt'); %Import data
Y1=load('D:My DocumentsMATLABdens_flow_ejieRF2.txt'); %Import data
Xcorr_size=512; % defines the length of the cross-correlation
Xk=zeros(1,2*xcorr_size);
Yk=zeros(1,2*xcorr_size);
Label_x=zeros(1,2*xcorr_size);
Velo= zeros(1,2*xcorr_size);
Xk(1:xcorr_size)=x1(1:xcorr_size); The following are the comparison experiments. The comparison will be made by using the fft correlation algorithm and the XCORR implementation. It is found that the correlation can be achieved without using the reverse folding method.
Yk(1:xcorr_size)=y1(1:xcorr_size); % achieves very good results
XK_FFT=fft(xk);
YK_FFT = conj(fft(yk)); % find conjugate, just add a conjugate operation before complex multiplication
ZK= XK_FFT.*YK_FFT;
Rxy=fftshift(ifft(ZK)); % is the same as taking the real part
Figure;
Plot(rxy);
TItle ('fft algorithm achieves linear correlation');
Rxy2=xcorr(xk(1:xcorr_size),yk(1:xcorr_size));
Figure;
Plot(rxy2);
TItle ('matlab comes with the correlation function xcorr result');
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