In Fast Convolution the filtering is performed by taking FFT of both the signal and impulse response and multiplication in frequency domain using Overlap add/Overlap save method for processing continuous signals. My question is what role if any does windowing (e.g. Blackman, Hanning etc.) play before taking the FFT of the signal and impulse response?
what role if any does windowing (e.g. Blackman, Hanning etc.) play
None. If you do apply a window (other than rectangular) for a regular overlap add/save algorithm, your results will be wrong.
Time domain windowing can be helpful if your frequency domain processing is time variant, but that requires more complicated algorithm with partially overlapping and fully reconstructing window & hop size.
It pretty much doesn’t. One could say a boxcar window is used, but you most likely won’t hear any mention it. The trick with doing FFT convolution is making sure your FFT length is at least equal to the number of signal samples plus the impulse response length minus one. Both your input signal and impulse response need to be padded with zeros appended to the ends to match the FFT length, which is sort of like a boxcar window. The reason we don’t call it windowing is because windowing is generally applied to deal with spectral leakage during analysis, or limiting time domain response during synthesis, which doesn’t apply here.
The term "Hanning" is illiterate. The window is attributed to Julius von Hann. So it is a Hann window, or von Hann window.
If you use overlap add/save fast convolution on von Hann windowed data where the windows are 50% overlapped, you get the same result as rectangular windows of data that are non-overlapped, except for the initial and ending transients.
You can also use 75% overlap if you don't mind a 2X gain. Or Hamming windows if you don't mind another roughly 2% gain.