Wavelet representations for time-frequency concentrated signals

Abstract

Time-frequency concentrated signals are defined in the paper as the class of signals whose Wigner distributions are concentrated in some region of the Wigner domain. The authors introduce the concept of the Kolmogorov n-width and the constrained n-width to quantitatively measure the ability of a basis to represent a time-frequency concentrated signal class (the cone-class signals). They select the best wavelet representation by comparing the constrained n-widths of different wavelet bases. An explicit formula is given to compute the Kolmogorov n-width for the cone-class signals. A globally convergent algorithm is proposed to calculate the constrained n-width for a given basis.<>