File:Hall2006 Logons.png

Summary
Heisenberg boxes convey the concept of varying time and frequency localization by visualizing an idealized time-frequency plane. (a) In the so-called Dirac basis the Heisenberg boxes become infinite vertical lines. (b) On the other hand, in the Fourier basis the spectrum is unlocalized in time. (c) The Fourier transform with a short time window gives poor localization in frequency. (d) A long window gives better frequency localization at the expense of time localization. (e) Wavelet transforms, and the S transform, have frequency- dependent localization: low frequencies are well localized in frequency but poorly localized in time, while the reverse is true for high frequencies.