How to convert from (diagonal matrix to criculant matrix) and Vice versa

Theoretically when applying Fourier transform on a circulant matrix, the result will be a diagonal matrix, and the opposite operation is also work. When using (fft) or (ifft) functions in Matlab the result isn't the same as the theoretical, can any body help

Answer 1

[Matt J]

Not sure what theoretical result you're citing. It is true that if you do an FFT of all the columns of a circulant matrix followed by an IFFT on all the rows, you will get a diagonal matrix, and the following illustrates that.

>> C

C =

       2     1     0     1
       1     2     1     0
       0     1     2     1
       1     0     1     2

>> ifft(fft(C).').'

ans =

       4     0     0     0
       0     2     0     0
       0     0     0     0
       0     0     0     2

Answer 2

[Abdelrahman Marconi]

Thank you for you answer but why you used 2 Fourier transform instead of one.

[Matt J]

Yes.