Minimum-bandwidth discrete-time wavelets

Abstract

In this paper we present a class of minimum-bandwidth, discrete-time orthonormal wavelets (MBDTWs). The wavelets were generated via the filter bank framework and were optimized using the global optimization technique, adaptive simulated annealing (ASA). The objective function is the average normalized bandwidth of the wavelets over all scales as obtained from the filter bank structure. We tabulate the wavelet-defining low-pass filter coefficients { g( n)} for filter lengths of N=4, 8, 10, 12, 14, 16, 18, 24 and 32 and for L=2, 3 and 4. We provide comparisons with Daubechies’ discrete wavelets and other classes of optimum wavelets. Finally, we present examples that demonstrate the advantage of our MBDTWs for certain narrowband applications: de-noising of an ECG signal, and compression of an ECG signal and a bird call signal. We compare the performance of our wavelets in these examples with that of Daubechies’ least-asymmetric wavelets which are closest to the MBDTWs with respect to our bandwidth measure.