How to get inverse discrete time Fourier transform (IDTFT) of an array?

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Palguna Gopireddy
Palguna Gopireddy 2022-7-23
评论： Palguna Gopireddy 2022-7-27
Apparently, there is no function to get IDTFT of an array. Is there any?
I used 'freqz(array,1)' to find the DTFT of an array from '0' to 'pi-pi/512'.
I also developed a code for DTFT for ab array A of length N from '-pi' to 'pi'
i=1
for wval=-pi:pi/512:pi
DFT(i)=sum(a.*exp(-1j*(0:N-1).*wval));
i=i+1;
end
But I do not know how to find IDTFT, when applied on a DTFT giving the original array.

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采纳的回答

Abderrahim. B
Abderrahim. B 2022-7-23
Ran in:
Hi!
Are you trying to implement DFT and its IDFT based on their equations ?
There are optimized algorithms to calculate these equations, the very well known one is the Fast Fourier Transform(FFT) and its inverse (IFFT). You may need to refer to this link for more explanation .
Demo:
Array = [1 2 3 4 5] % Sequence
Array = 1×5
1 2 3 4 5
arrFFT = fft(Array) % DFT based FFT
arrFFT =
15.0000 + 0.0000i -2.5000 + 3.4410i -2.5000 + 0.8123i -2.5000 - 0.8123i -2.5000 - 3.4410i
Array = ifft(arrFFT )
Array = 1×5
1 2 3 4 5
Hope this helps
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Abderrahim. B
Abderrahim. B 2022-7-27
编辑：Abderrahim. B 2022-7-27
Ran in:
Use fft2 and ifft2.
A = [1,2,3; 4,5,6] ;
[n_row, n_col ] = size(A) ;
A_2Dfft = fft2(A, 512, 512) ;
A_ifft2 = ifft2(A_2Dfft) ;
reconst_A = A_ifft2(1:n_row, 1:n_col) ;
isequal(reconst_A , A)
ans = logical
1
Palguna Gopireddy
Palguna Gopireddy 2022-7-27
Thanks @Abderrahim BELISSAOUI.
But I can't prove the convolution theorem for 2D.
I posted it as another question. Could you help me withis this.
https://in.mathworks.com/matlabcentral/answers/1768915-can-t-prove-the-convolution-theorem-of-fourier-theorem-for-two-dimensional-matrices

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