I need some clue on how to apply the Fourier transform to a wideband discrete signal like speech in Matlab. What I want to do is to apply the MUSIC algorithm to the speech recorded by a set of microphones and in order to do that I need to take the FFT and then apply the MUSIC algorithm to the bins of frequencies which now I consider them narrowband .
You can take the samples of the speech satisfying Nyquist criterion. Say you got a vector of samples called x. spectrogram(x) would give you the short time Fourier Transform of x. fft(x) would give you the dft of the speech signal in a more computation-efficient manner compared to direct computation.
Also see help fft and choose whatever you want.