Inverse FFT - Synch the Phase Is there any way to synchronize phase of output of inverse DFT in each buffer? When I send the output of inverse DFT to the speaker it sounds nasty.

Of course I know the windowing functions but it just gives me in/decreasing level at the beginning and the end of buffer. It sounds better but with tremolo effect. I’ve also heard about overlapping windowing, I haven’t tried that but I am pretty sure it also won’t give me clean signal. Probably it will give me some phasing/chorusing effect that will appear periodically on each beginning and end of buffer. So I wonder how to repair that?
If you were attempting to modify the contents of a DFT before the inverse DFT, say for filtering, then you need to do overlap-add or overlap-save fast convolution instead of just an Inverse DFT.  You will also need to use a longer DFT and inverse DFT.  If you can determine the length of the impulse response of your filter, then the length of the new DFT/IDFT needs to be extended and zero-padded by the length of that impulse response, so that the filter convolution is equivalent to linear, not circular.

If filtering, the noise you hear is likely the result of doing a circular convolution, instead of zero-padding and overlapping.

If, instead you are synthesizing audio, look up phase vocoder methods.