Kolmogorov n-widths and wavelet representations for signal classes

We address the problem of basis selection and wavelet representations for two important signal classes: the ellipsoidal signal class and the bounded cone class. We define time-frequency concentrated signals in this paper as the class of signals whose Wigner distributions are concentrated in some region of the Wigner domain. We use the concept of the Kolmogorov n-width and the constrained n-width to quantitatively measure the ability of a basis to represent a signal class. We select the best wavelet representation by comparing the constrained widths of different wavelet bases. Explicit formulas are given to compute the Kolmogorov n-width for both signal models. A globally convergent algorithm is proposed to calculate the constrained n-width for a given basis.