Time–frequency uncertainty

No signal can be arbitrarily well localized in both time and frequency at once: the product of a signal's time spread and its frequency spread is bounded below (the Gabor limit, the signal-processing analogue of the Heisenberg inequality). A short analysis window pins down when an event happened but blurs its frequency; a long window resolves frequency finely but smears the timing. Every time-frequency method, whether the short-time Fourier transform, wavelets or Hilbert filtering, is a particular choice on this frontier.

The tiling of the time-frequency plane makes the choice concrete: the STFT uses a fixed window, so all cells have the same shape, whereas the wavelet transform uses windows that shrink at high frequency, giving good timing for fast events and good frequency resolution for slow ones. There is no universally best tiling; the right one depends on whether the phenomenon of interest is a sustained rhythm or a brief transient.