Say I have a signal of length 20s that contains signal from various (unknown) biological sources, e.g. heartbeat (~0.2Hz), respiration (~1Hz), and possibly som very-low frequency oscillations (~0.05Hz). My sampling frequency is fs=10Hz. I conduct a periodogram PSD estimate (hanning window, mean-subtracted, N_FFT=500), yielding a spectrum with frequencies 0:0.02:5 Hz.

Say I have several 20s recordings in two different settings and I want to conduct a statistical analysis of the spectral power in specific frequency bins or bands. Is there a lower limit to which frequencies I can use to statistically infer on biology?

For example, should I assume there to be a specific number of periods of frequency present in the window? E.g., if I say that at least 2 periods should be present in the window, the lowest detectable frequency is 0.1Hz. Or can I just as easily infer on the spectral power of frequencies as low as my resolution allows?


1 Answer 1


If the goal is to map out a range of low frequencies, then CWT is preferred over STFT, as it zooms logarithmically and will provide far more detail (examples). If the goal is a few specific frequencies, then a targeted STFT will work (i.e. design windows for said frequencies rather than doing a linear sweep).

What remains is boundary effects: large windows demand data beyond the span of original input. The answer is padding, but no single perfect scheme: any method (including zero padding) is akin to imposing a statistical prior, i.e. assumption to best-fit the source process.

  • I've done much work on this subject and can recommend reflect as the best general scheme, if nothing else is known. Related post, discussion
  • However, if the goal is instantaneous frequency/amplitude localization, zero might be favorable (see examples).
  • For an advanced approach, see boundary wavelets.

Best results will integrate domain knowledge into the application - i.e., use the "best guess" for how the source behaves outside the measurement. If the source isn't sufficiently oscillatory to begin with, methods other than CWT/STFT may be favorable.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.