Reconstruction of a Signal from the Real Part of Its Discrete Fourier Transform for matlab

Hello, good work.

We need Reconstruction of a Signal from the Real Part of Its Discrete Fourier Transform for matlab. Can anyone help?

Answer 1

[MarKf]

N = 14; %ns = 0:N;
xn =  1/2*(randn(N, 1) +1i*randn(N,1)); %random complex signal
x_n = [0+0i;xn;zeros([N,1])+0i]; % M or numel(x_n)=2*N+1
X_k = fft(x_n);
Xr_k = real(X_k);
y_n = ifft(Xr_k*2);
subplot(221),plot(real(xn)), title('real part x(n)')
subplot(222),plot(imag(xn)), title('imag part x(n)')
subplot(223),plot(real(y_n(2:N+1))), title('real RDFT ~y(n)')
subplot(224),plot(imag(y_n(2:N+1))), title('imag RDFT ~y(n)')

[Furkan Seçkiner]

Hello sir, thank you for your reply. Is that the answer?

The signals did not change, do I need to do anything else?

Can you recommend any resources on this subject?

[MarKf]

Sorry for the late reply to this, I just quickly recreated in Matlab the simple formulas in the paper you provided, you can see the variables names and the figures matching. So I thought it did not need a follow up.

You can adapt the code to your needs, if you understand the code and the theory that is, if you need signal processing resources on theory and how it's done in Matlab, or intro to coding, this website offers both (e.g. mathworks.com/help/signal/) but also there's a lot online. Same if you are talking about the slightly more advanced topic of signal reconstruction.

Consider accepting the answer if that's what you were looking for or if it helped.

Answer 2

[Star Strider]

No.

You will need the complex part (or equivalently, the phase information) to accurately reconstruct the signal. Otherwise, taking the inverse Fourier transform of only the real part of the Fourier transform will produce something, although not the original signal.

[Furkan Seçkiner]

https://maxwell.ict.griffith.edu.au/spl/publications/papers/ieeespm18_so.pdf

Our subject is attached. We want to implement this issue with matlab.