Using a compilable programming language (not Librosa, Matlab, etc), I am attempting to perform ISTFT on filtered (masked) source STFT matrices obtained from NMF. During the original construction of the mixed STFT matrix, I am using a window length of 1024, and hop length of 512. When I run FFT on each window's $x(n)$ of length 1024, I can only use the first 512 amplitude and phase values returned, due to Nyquist.
After I generate filtered STFT's from each source after NMF, how can I estimate a $y(n)$ of length 1024 fin the time domain when I only have 512 inputs to IFFT? (The 512 inputs for each IFFT are the elements in each column of the filtered source-specific STFTs).
Should I keep the full 1024 coefficients returned from the original FFTs, and use a mixed STFT with dimensions $1024 \times \#windows$ as the basis for the entire analysis?
Last, the filtered source-specific STFT matrices will not provide real and complex values returned from an FFT, which are required for IFFT. Thus, my logic tells me OLA is a method to side-step IFFT.