Hi matt,
I think the issue is with how the padding is being done. See code below for that and other questions. Full disclosure: I'm only looking at how the fft/ifft is being used; I'm not familiar with this type of problem.
rng(100);
d1 = designfilt("lowpassiir",FilterOrder=12, ...
HalfPowerFrequency=0.02,DesignMethod="butter");
N = 2^10;
y1 = rand(N,1);
y1 = filtfilt(d1,y1)';
N2 = 2^2;
shiftImposed = 1*N2;
y2 = interp1((1:N),y1,(1+shiftImposed:N+shiftImposed));
y3 = imresize(y1,1/N2);
y4 = imresize(y2,1/N2);
y5 = y3(length(y3)/8:length(y3)-length(y3)/8+1);
y6 = y4(length(y3)/8:length(y3)-length(y3)/8+1);
figure(54);plot(y5);hold on;plot(y6)
Correlation without interpolation
g1 = y5-mean(y5);
g2 = y6-mean(y6);
G1 = fft(g1);
G2 = fft(g2);
R = G1.*conj(G2);
N = length(R);
p=0;
N2 = 2^p*N;
x = (1:N2);
% no padding here
N2 - N
R2 = padarray(R,[0 (N2-N)/2] ,0,'both');
Why is fftshift applied here?
rr2 = fftshift(ifft(R2,'symmetric'));
figure(43);plot(abs(rr2))
Correlation with 2N interpolation via zero padding ifft of cross power spectrum
g1 = y5-mean(y5);
g2 = y6-mean(y6);
G1 = fft(g1);
G2 = fft(g2);
R = G1.*conj(G2);
N = length(R);
p=1;
N2 = 2^p*N;
x = (1:N2);
% pad with this many 0's in both directions
N2-N
I think the issue is here. Need to fftshift R, and then pad the left and the right for negative and positive frequencies, and then ifftshift back for use with ifft in the next step.
%R2 = padarray(R,[0 (N2-N)/2] ,0,'both');
R2 = ifftshift(padarray(fftshift(R),[0 (N2-N)/2] ,0,'both'));
Why is fftshift applied here?
rr2 = fftshift(ifft(R2,'symmetric'));
figure(43);plot(abs(rr2))
