Minimum bandwidth basis functions for the fourth-moment bandwidth measure

Abstract

We present a fourth-moment measure of the "bandwidth" of a strictly time-limited signal and obtain a minimum bandwidth basis for /spl Lscr//sup 2/(a,b). Such a basis consists of orthonormal waveforms with the smallest obtainable bandwidths. The primary advantage of the fourth-moment bandwidth relative to the root mean square (RMS) and fractional out-of-band energy (FOBE) measures is that its basis functions have a O(1/f/sup 3/) frequency roll-off compared to the O(1/f/sup 2/) and O(1/f) decay of the RMS and FOBE basis functions, respectively.