Get time signal back after NFFT

Hello,

I have the following code, which generate a complex chirp signal.

fs = 200e6
t=0:1/fs:1e-3;
f0=1;
f1=2e6; 
t1 = 1e-3;

i = mychirp(t,f0,t1,f1); 
q = mychirp_sine(t,f0,t1,f1);
x = complex(i,q);

L = length(x);
NFFT = 2^nextpow2(L)*4;

X = fftshift((fft(x,NFFT)));
f = fs*(-NFFT/2:NFFT/2-1)/NFFT;

Here is what I got in time domain and frequency domain :

Now I would like to go back in the Time domain after my FFT computed with the factor NFFT. Does anyone know how to compute the time vector in order to plot(timeVector,ifft(X)) ? I would like to plot my original signal after the IFFT.

Thank you.

Answer 1

[Christoph F.]

The time vector as as many elements as X, and they are spaced 1/(f(2)-f(1)) apart.

And you will probably need to reverse the fftshift performed on X with ifftshift(X) before doing an ifft.

[So]

X has 1 048 576 elements. My original signal's duration is 1ms (from 0:1/fs:1e-3). So my original time vector has 2001 elements. When I perform an ifft on X, it still has the 1048576 elements compared to my orignal time vector of 2001 elements... If I create a new time vector 0:1/(f1-f0):1e-3 it will still has 2001 elements.

[Christoph F.]

I see it now.

In that case, transforming back to the original time domain signal requires knowledge of the original sampling rate and the number of padding samples used in fft(). This information can no longer be determined from the vector f.

One approach would be:

1. Transform back to the zero-padded signal

xc = ifft(ifftshift(X))

2. Remove the padding zeros

xc = xc(1:length(x))