I have been trying to understand the weighted overlap-add (WOLA) method. By searching papers and posts in dsp.SE, I found that the window length can be larger and smaller than the FFT size.
1. Window length larger than FFT size.
See the comment in this post. It says that "WOLA allows you to use an N-point DFT with an MN-point analysis window". I wonder how one can do a N-point DFT with an MN-point window since the FFT size is N. How many data points in one frame should we use, N or MN? (I know this is possible with DTFT because we can calculate the STFT at N frequency bins using a MN-point DTFT with the definition, but how to do it with FFT?)
2. Window length smaller than FFT size.
See the Fig.1 of this paper. It uses a window h(m) that is less than the FFT transform size. In this case, the data at both ends of a frame are not weighted. Is it the same as padding zero at both ends? From the figure, it is not the case because M samples of input are used. If it is zero-padding, then we only have to input data samples with the same length with h(m). So how are data at ends processed?
What am I missing with these questions? Thank you!
For convenience, a snapshot of Fig.1 is attached here.