WAVELET TRANSFORM ALGORITHMS FOR FINITE-DURATION DISCRETE-TIME SIGNALS

The algorithms split for the wavelet transform and merge for the inver se wavelet transform are presented for finite-duration discrete-time s ignals of arbitrary length not restricted to a power of 2. Alternative matrix- and vector-filter implementations of alternative truncated, c irculant, and extended versions are discussed. Matrix- and vector-filt er implementations yield identical results and enhance, respectively, didactic conceptualization and computational efficiency. Truncated, ci rculant, and extended versions produce the signal-end effects of, resp ectively, errors, periodization, and redundancy in the transform coeff icients. The use of any one of these three versions avoids the signal- end effects associated with the other two versions. Additional alterna tives that eliminate all signal-end effects (albeit at the cost of inc reased algorithmic complexity) are discussed briefly.