why convolution of x and y is different ifft(fft(x)xfft(y))?

Question

I know that convolution of x and y in time domain is equal to fft(x) times by fft(y) in frequency domain. so I tried simple example using matlab as below.

xn=[1,2,3,4];
yn=[4,3,2,1];
zn=conv(xn,yn);

znr=ifft(fft(xn).*fft(yn));

and I got the result as below.

zn = 4 11 20 30 20 11 4 znr = 24 22 24 30

I wonder why zn is not equal to znr. Anyone who knows why pls explain.

Answer 1

Specifying the transform length when taking the fft() to configure the solution in the way you want may be a solution. Since typically the result of convolution has a length that is equal to the sum of the two signals convolved subtract 1 we can then set the Transform_Length to 7 in this case.

xn = [1,2,3,4];
yn = [4,3,2,1];
zn = conv(xn,yn);

Transform_Length = length(xn) + length(yn) - 1;
znr = ifft(fft(xn,Transform_Length).*fft(yn,Transform_Length));

zn
znr

Result:

Ran using MATLAB R2019b