# 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.

FFT implicitly uses a rectangular window for a sequence. This kind of rectangular windowing has demerits. Rectangular window causes "leakage" of the main lobe power onto the side-lobes.

Windowing is one of the techniques to reduce the side-lobe level. However, there are drawback in windowing too. Windowing increases the width of the main lobe which in turn affects the resolution. Rectangular window has a good resolution, that is, a sharper main lobe compared to other windows.

Therefore, in windowing, there is a trade-off between the width of main lobe and power in the side lobes. This trade-off is studied in the signal processing literature and it is available in many digital signal processing text books.

• "FFT assumes that the values of the sequence are exactly zero outside the sequence" - I'm not convinced this is correct, FFT assumes a looping/repeating signal. Apr 14, 2014 at 5:52
• Yes I am wrong. Thanks for correcting me. FFT assumes the data is repetitive. Apr 14, 2014 at 7:51

Convolution with the transform of a Von Hann window generates a less noisy looking FFT spectrum result than does convolution with a rectangular window. One reason that this is so is because the Von Hann window attenuates the left and right sides of the data window so that there isn't a big difference between these two ends. This makes the signal easier to represent with lower frequency basis vectors that are close to the same value at the two ends of the window, as are periodic-in-window sinusoids.