What exactly is the effect of a Hann Window on the FFT output? In the code I am trying to understand, there is an usage of Hann window multiple times (There's overlapping frames, the size of each is 512 and the overlapping factor is 75% so each time we capture  128 samples we build a new frame by shifting the previous one by 128 to the left). For each Frame we apply a Hann window before the FFT, so the first 128 samples were actually "framed" 4 times.

However I don't understand the purpose of this windowing. Can someone please tell me what its effect is on the FFT ?
See the following: http://www.dtic.mil/dtic/tr/fulltext/u2/a381695.pdf  especially p.631 Figs. 17+18.  As noted by the author, a 4 to 1 overlap using a Hann or Hamming window allows for proper reconstruction.

Also see: F. J. Harris, “On the use of Merged, Overlapped and Windowed FFT’s to Generate Synthetic Time Series Data with a Specified Power Spectrum,” Proc. IEEE 16th Asilomar Conf., 1982, pp. 316-321.