Implementing short-time Fourier transform
admittedly, i have never used the buffer() function in matlab.  for doing STFT analysis and processing, i have just broken it into frames myself with code similar to this answer.  it's easier to see what's going on.

while you can use a gaussian window for analysis (i found it mathematically useful in this paper, email me if you want a pdf copy), you must use a complementary window, one that adds to 1 with the windows of its adjacent frames, for the reconstruction of the signal.  at least if you want this to pass the signal unchanged when the processing is set to "null".