Minimum-bandwidth discrete-time wavelets

In this paper we present a class of minimum-bandwidth, discrete-time orthon ormal wavelets (MBDTWs), The wavelets were generated via the filter bank fr amework and were optimized using the global optimization technique, adaptiv e simulated annealing (ASA). The objective function is the average normaliz ed bandwidth of the wavelets over all scales as obtained from the filter ba nk 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 f or L = 2, 3 and 4. We provide comparisons with Daubeohies' discrete wavelet s 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 w ith that of Daubechies' least-asymmetric wavelets which are closest to the MBDTWs with respect to our bandwidth measure. (C) 1999 Elsevier Science B.V . All rights reserved.