Time-frequency localization for sequences
Milos I. Doroslovacki, Hong Fan, Petar M. Djurić · 2003
Two second-moment-type quantities characterizing the localization of a sequence in discrete time and in frequency are introduced. Their product satisfies an uncertainty relation. The sequences that reach the lowest uncertainty level are found. In an appropriate limit case for the transition from discrete-time to continuous-time-signals, those sequences tend to the Gaussian signal. The second and corresponding first moments are physically interpreted. In frequency, the interpretation is related to the center of gravity and moment of inertia of a unit-mass ring. In time, it is based on the ordinary first and second moments of specially filtered as well as nonfiltered original sequences.>