Fourier transform of a sine wave, width of the spectral peak

General Usage
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Hello all! I was wondering, if I’ve got the Fourier transform of a sine wave, how would I calculate the width of that Fourier transform in Julia? Is there a package that does that written in Julia? An example from SciPy is
https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.peak_widths.html|https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.peak_widths.html

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Assuming that the FFT of the sine wave exhibits spectral leakage as in figure below, a very simple procedure produces the approximate width of the spectral peak (no bells and whistles):

  • Compute the magnitude of the FFT (may taper the original signal and pad it with zeros for better spectral definition)
  • find both the peak frequency and max spectral amplitude with findmax()
  • count the frequency bins above a given threshold from that maximum with count()

The example below looks for amplitudes above -20dB from spectral maximum, which was normalized to 0 dB:

Spectral_leakage_width
Spectral_leakage_width1998×819 142 KB