Zero padding - before or after the windowing?

Question

I am trying to perform the STFT on a speech signal. I'd like to know when I should do the zero-padding, before windowing each frame, or after?

My attempt:

x    = signal(:);                   % make sure signal is a column vector
sL   = length(x);                   % signal length
wL   = fix(window_Time*fs);         % window length
HOP  = floor(wL*(1 - overlap/100)); % windowing step 
win  = gausswin(wL);                % window type
F    = 1 + fix((sL-wL)/HOP);        % calculate the number of signal     frames
stft = zeros(nfft,F);               % preallocate stft matrix, [nfftxF]

for f = 0:F-1
    xw          = x(1+f*HOP:wL+f*HOP).*win; % windowing
    X           = fftshift(fft([xw;zeros(wL,1)],nfft));   % FFT shifted (double-sided)
    stft(:,1+f) = X;                        % update of the stft matrix
end

Answer 1

You must do it before the FFT.

1. Divide the signal into frames, see butter function;
2. Apply a window to each frames: frames x window;
3. Zero-padd the signal;
4. FFT each windowed frames.

P.S. I've read somewhere that the FFT algorithm already does the zero-padding automatically, i.e., When you to the FFT(x) it will already “padd” the signal x with zeros at the end, to reach the length of the FFT.