Algorithm 735

Algorithm 735: Wavelet transform algorithms for finite-duration discrete-time signals. The algorithms split for the wavelet transform and merge for the inverse wavelet transform are presented for finite-duration discrete-time signals of arbitrary length not restricted to a power of 2. Alternative marix- 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. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Průša, Zdeněk; Søndergaard, Peter L.; Rajmic, Pavel: Discrete wavelet transforms in the large time-frequency analysis toolbox for MATLAB/GNU Octave (2016)
  2. Ko, Kyungduk; Qu, Leming; Vannucci, Marina: Wavelet-based Bayesian estimation of partially linear regression models with long memory errors (2009)
  3. Benkrid, A.; Benkrid, K.: Handling finite length signals borders in two-channel multirate filter banks for perfect reconstruction (2006)
  4. Uhl, Andreas; Pommer, Andreas: Image and video encryption. From digital rights management to secured personal communication (2005)
  5. Vannucci, M.; Brown, P. J.; Fearn, T.: A decision theoretical approach to wavelet regression on curves with a high number of regressors (2003)
  6. Feil, Mafred; Uhl, Andreas: Wavelet packet image decomposition on MIMD architectures (2002)
  7. Feil, Manfred; Uhl, Andreas: Real-time image analysis using MIMD parallel à trous wavelet algorithms (2001)
  8. Baharav, Zachi; Leviatan, Yehuda: Impedance matrix compression using adaptively constructed basis functions (1996)
  9. Brislawn, Christopher M.: Classification of nonexpansive symmetric extension transforms for multirate filter banks (1996)
  10. Uhl, Andreas: Wavelet packet best basis selection on moderate parallel MIMD architectures (1996)
  11. Nason, G. P.: Choice of the threshold parameter in wavelet function estimation (1995)
  12. Nason, G. P.; Silverman, B. W.: The stationary wavelet transform and some statistical applications (1995)
  13. Taswell, Carl: WavBox 4: a software toolbox for wavelet transforms and adaptive wavelet packet decompositions (1995)
  14. Taswell, Carl: Top-down and bottom-up tree search algorithms for selecting bases in wavelet packet transforms (1995)
  15. Taswell, Carl; McGill, Kevin C.: Algorithm 735: Wavelet transform algorithms for finite-duration discrete-time signals (1994)