Time, frequency, sequency, and their uncertainty relations (Corresp.)

Abstract

We study the form assumed by the classical time-frequency uncertainty relations in discrete as well as nontrigonometric spectral analysis. In particular we find that if anN-sample time signal is to contain a fractiongammaof its energy inTconsecutive samples, then the minimum number of frequency components containing that same energy fraction must be greater thanN/T(2gamma - 1)^2. It is also found that the discrete Walsh transform permits greater energy concentration (less uncertainty) than the discrete Fourier transform.