Recontruct temporal signal from FFT after transformations

Hello and thank you for taking time on this,

I have a temporal audio signal of 1 second, at 48kHz. I perform an fft on this signal to be able to apply some frequency-dependent modifications on the Spectrum. Then i would like to recreate a temporal signal using these modified amplitude and phase. My problem is that i don' t see how i can recontruct a whole temporal signal, of the same intital length (1 second), if i only use 1024, 2048 or 4096 points for my Fft calculations. So far my code is :

 FS=48000;
 TS=1/FS;
 time=1; %temporal length
 vec_t=[0:TS:time]';
 vec_t=vec_t(1:end-1);
 SIG_0=wgn(length(vec_t),1,0); % source signal

Spectrum computation, modification, reconstruction :

 Nfft=4096;
 f_lim=Fs/2; %nyquist frequency 
 df=Fs/Nfft;
 f=-f_lim:df:f_lim-df;

 F1=a1'.*fftshift(fft(SIG_0(:,1),Nfft)); %With a1 a complex number for Spectrum modification
 S1=ifft(ifftshift(F1));

This code works fine, but as you can see, my reconstrcuted signal S1 is only made of Nfft-samples. Is there a matlab function that can reconstruct a whole temporal signal ? may be using windowed-averaged fft ?

Answer 1

[Julia Antoniou]

Hi Benoit,

There is no windowed-averaged or moving average function specific to FFT. I would recommend using the "movmean" function. (https://www.mathworks.com/help/matlab/ref/movmean.html)

You could also make your "Nfft" the next power of two greater than 40,000, which is 65,536. Although your signal "SIG_0" is only 40,000, the FFT functions will know to pad the rest of the signal with zeros. These zeros can be truncated once your calculations are complete.