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

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 an
N
-sample time signal is to contain a fraction
\gamma
of its energy in
T
consecutive samples, then the minimum number of frequency components containing that same energy fraction must be greater than
N/T(2\gamma - 1)^2
. It is also found that the discrete Walsh transform permits greater energy concentration (less uncertainty) than the discrete Fourier transform.