I made a quick test,
original first, then resynthesized with time stretch and pitch shift and corrected formants:

https://soundcloud.com/traumlos_kalt/ft-resynth-test-1-01/s-7GCLk
https://soundcloud.com/traumlos_kalt/ft-resynth-test-2-01/s-2OJ2H

sounds quite phasey and gurgely
I am using 1024 FFT size and 5 bins moving average to extract a
spectral envelope for formant preservation, which is probably not the best way to do this

I assume you would need to realign phases at transients
sound quality isn't what you would expect in 2018...
(also I am doing the pitch shift the wrong way at the moment,
first transpose in time domain, then FFT time stretch, cause that was easier to do for now
but this shouldn't cause an audible problem here)

about latency I dont now yet, I am using my FFT for NI Reaktor which has a latency of several times FFT size
and is only good for proof of concept stuff


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