STFT - Putting it all together

Question

I'm currently reading this paper: http://www.rssd.esa.int/SP/LISAPATHFINDER/docs/Data_Analysis/GH_FFT.pdf

On page 21, it has a section called "Putting it all together", it states the following steps:

Input data

Frequency resolution and length of DFT

Window function

Splitting of the data stream

FFT

Scaling

Now, the "Window function" is mapped out before the "Splitting of the data stream" if this is the case, should I therefore multiply each of the bins within the data stream by each of the window values (Hanning)?

For example, at the moment, my Hanning window size is: 256 and the data is split into segments of size 256x128 in this case.. N = size of stream and then compute hanning(N)

I've seem a lot of DSP engineers split the window up into frames, before applying the window?

Thanks

Answer 1

If your window is a rectangular window, then there is no mapping out since splitting the stream into frames is effectivley applying that window. Once you split the stream into frames, if your window is not rectangular, you would then multiply the window against the frame.

y[i] = x[i] * w[i], for i = 0 to N-1, then take the FFT of y.

Answer 2

A non-rectangular window function is usually to help compensate for some of the effects of splitting the stream (which ends up being a rectangular window). So the window function is to be applied after splitting the stream into FFT length (or shorter) blocks.