This link gives the procedure of implementing the WOLA method. It can be summarized briefly as windowing the extractd data frame, FFT, modify the spectrum, IFFT and overlap-add the windowed IFFT result to the reconstructed data buffer.
Suppose the modification to the spectrum of each data frame in the WOLA is time-invariant linear filtering, i.e., fast convolution is applied to the FFT of the windowed data. From the procedure of the WOLA, no zero-padding is used to the windowed data prior to FFT, thus there will be circular convolution alias when we multiply the FFT of the filter to the data FFT and IFFT.
However, if we zero-padd the windowed data before FFT, the length of data after IFFT will be increased. In this case, we cannot use a synthesis window of the same length (with the analysis window) to scale the IFFT result so as to guarantee perfect reconstruction. But as the procedure points out, the synthesis window is usually the same as the analysis window. Thus it seems impossible to obtain the same filtering result as that of convoluting the long data directly with a linear filter.
What's the problem with my understanding? Hope you point out.
