MATLAB: IFFT of Convolution equivalence

complex numbersconvolutionfftifftMATLAB

I was trying out the equation IFFT(x*y) = IFFT(x).IFFT(y), where both 'x' and 'y' are complex numbers. The 'x' and 'y' are 1×8 matrices. The result was different for both sides of the equation. However i was able to prove that x*y = IFFT[ FFT(x).FFT(y)] and FFT(x*y)=FFT(x).FFT(y). What did I miss out when I tried to solve the IFFT relation? Please let me know of any source that has helpful content regarding this relationship

Best Answer

Sorry for the confusion. Here is what I tried:
a1 = randi(50,8,1);
b1 = randi(50,8,1);
x = complex(a1,b1)
a2 = randi(50,8,1);
b2 = randi(50,8,1);
y = complex(a2,b2)
xifft = ifft(x)
yifft = ifft(y)
mifft = xifft.*yifft
z = cconv(x,y,length(x))
zifft = ifft(z)./length(z)
% zifft-mifft is almost zero
Summary: you need circular convolution in frequency domain instead of linear convulation.
More details:
https://www.mathworks.com/matlabcentral/answers/59333-convolution-in-frequency-domain-not-convolution-in-time-domain?s_tid=answers_rc1-2_p2_MLT
https://www.mathworks.com/matlabcentral/answers/38066-difference-between-conv-ifft-fft-when-doing-convolution?s_tid=answers_rc1-3_p3_Topic
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