FFT analysis bandwidth (window length)
This is a small demonstration
of the time/frequency resolution trade-off inherent in fast fourier analysis.
You can vary the analysis bandwith of the spectrogram to get either good
frequency resolution or good time resolution, but not both at the same
time for a given bandwidth. This is easiest seen for a short sine pulse.
An analysis bandwidth of 500 Hz gives a good match to the waveform regarding
time localization. However, the frequency estimate is quite blurred. On
the other hand, a 20 Hz bandwidth gives much better frequency resolution,
but at the cost of poorer time localization. An ideal spectrogram of the
signal is shown at the bottom. Fourier analysis is really only well-defined,
mathematically, for periodic waveforms. For a sine with much longer duration,
which is a better approximation to a periodic wave, a 20 Hz bandwidth gives
a much better match to the ideal case.
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