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Good morning, I have a simple question about the application of a Hanning window before performing an FFT. My application is pretty textbook, i'm decoding a 4-FSK signal.

Question: why does the spectral width increase when I apply a Hanning window to a perfect sin?

Many thanks! ASignal with Hanning window

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Generally, any window (rectangular or Von Hann) convolves the input with the transform of the window.

The transform of a rectangular window is a Sinc shaped "ringy" waveform with infinite ripples, but these side lobes are invisible for pure sinusoids that are exactly integer periodic in the FFT width.

Smoother windows have lower ripples, but in exchange have wider main lobes.

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