Algorithm 735

Algorithm 735: Wavelet transform algorithms for finite-duration discrete-time signals The algorithms {it split} for the wavelet transform and {it 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: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 14 articles , 1 standard article )

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