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I'm computing 1 sec. hanning windows from a signal that has a variable frequency between 1-4Hz. My first impression is that data loss caused by the distortion due to the window function is greater than the correction that it is expected to give while taking FFT of that window. Am I right?

Is it a bad approach to apply window functions to such windows with size of at most 4 wavelengths?

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A 1s Hann window will have (in the frequency domain) a main lobe width of 4Hz. This will severely mask your signal components.

Even a rectangular window will be ~2Hz main lobe.

You should use a greater windowing time depending on the accuracy you need for frequency detection.

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A von Hann window does not "correct" the results of an FFT.

It (1) reduces interference from other portions of the spectrum in the window's stop-band at the cost of (2) reduced resolution (due a fatter main lobe in the frequency domain) and less total information.

You have to trade-off the 2 effects for your particular situation.

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