Uncertainty relations involving ordinary second moments in time and frequency for discrete-time signals

Abstract

In the discrete-time case, the product of the ordinary second moments of signal-energy distribution in time and frequency does not satisfy the Gabor uncertainty relation, in the sense that there is no strictly positive uncertainty limit. E.g., for the unit sample sequence, the product is zero. For specially defined second moments, the Gabor uncertainty relation is satisfied (Doroslovački, Signal Processing 67 (1) (May 1998) 59). We are presenting here new results showing valid uncertainty relations involving one ordinary second moment. The results are important for conceptualization and characterization of the simultaneous time–frequency localization for sequences.