Algorithm 735: Wavelet transform algorithms for finite-duration discrete-time signals
Carl Taswell, Kevin C. McGill · ACM Transactions on Mathematical Software · 1994
The algorithms split for the wavelet transform and merge for the reverse wavelet transform are presented for finite-duration discrete-time signals of arbitrary length not restricted to a power of 2. Alternative matrix-and vector-filter implementations of alternative truncated, circulant, and extended versions are discussed.Matrix-and vector-filter implementations yield identical results and enhance, respectively, didactic conceptualization and computational efficiency.Truncated, circulant, and extended versions produce the signal-end effects of, respectively, errors, periodization, and redundancy in the transform coefficients The use of any one of these three versions avoids the signal-end effects associated with the other two versions.Additional alternatives that eliminate all signal-end effects (albeit at the cost of increased algorithmic complexity) are discussed briefly.