Skip to content


  • Research Article
  • Open Access

Fixed Wordsize Implementation of Lifting Schemes

EURASIP Journal on Advances in Signal Processing20062007:013754

  • Received: 16 December 2005
  • Accepted: 26 August 2006
  • Published:


We present a reversible nonlinear discrete wavelet transform with predefined fixed wordsize based on lifting schemes. Restricting the dynamic range of the wavelet domain coefficients due to a fixed wordsize may result in overflow. We show how this overflow has to be handled in order to maintain reversibility of the transform. We also perform an analysis on how large a wordsize of the wavelet coefficients is needed to perform optimal lossless and lossy compressions of images. The scheme is advantageous to well-known integer-to-integer transforms since the wordsize of adders and multipliers can be predefined and does not increase steadily. This also results in significant gains in hardware implementations.


  • Information Technology
  • Quantum Information
  • Wavelet Coefficient
  • Discrete Wavelet
  • Significant Gain

Authors’ Affiliations

Department of Electrical and Computer Engineering, College of Engineering, Texas Tech University, P.O. Box 43102, Lubbock, TX 79409-3102, USA


  1. Daubechies I, Sweldens W: Factoring wavelet transforms into lifting steps. Journal of Fourier Analysis and Applications 1998,4(3):247-269. 10.1007/BF02476026MathSciNetView ArticleGoogle Scholar
  2. Calderbank AR, Daubechies I, Sweldens W, Yeo B-L: Wavelet transforms that map integers to integers. Applied and Computational Harmonic Analysis 1998,5(3):332-369. 10.1006/acha.1997.0238MathSciNetView ArticleGoogle Scholar
  3. Mertins A, Karp T: Modulated, perfect reconstruction filterbanks with integer coefficients. IEEE Transactions on Signal Processing 2002,50(6):1398-1408. 10.1109/TSP.2002.1003063View ArticleGoogle Scholar
  4. Oraintara S, Chen Y-J, Nguyen TQ: Integer fast Fourier transform. IEEE Transactions on Signal Processing 2002,50(3):607-618. 10.1109/78.984749MathSciNetView ArticleGoogle Scholar
  5. Liang J, Tran TD: Fast multiplierless approximations of the DCT with the lifting scheme. IEEE Transactions on Signal Processing 2001,49(12):3032-3044. 10.1109/78.969511View ArticleGoogle Scholar
  6. Malvar H, Sullivan G: YCoCg-R: a color space with RGB reversibility and low dynamic range. ISO/IEC JTC1/SC29/WG11 and ITU-T SG16 Q.6, July 2003Google Scholar
  7. Geiger R, Yokotani Y, Schuller G: Improved integer transforms for lossless audio coding. Proceedings of the 37th Asilomar Conference on Signals, Systems and Computers (ACSSC '03), November 2003, Pacific Grove, Calif, USA 2: 2119–2123.Google Scholar
  8. Reichel J, Menegaz G, Nadenau MJ, Kunt M: Integer wavelet transform for embedded lossy to lossless image compression. IEEE Transactions on Image Processing 2001,10(3):383-392. 10.1109/83.908504View ArticleGoogle Scholar
  9. Adams MD, Ward RK: Symmetric-extension-compatible reversible integer-to-integer wavelet transforms. IEEE Transactions on Signal Processing 2003,51(10):2624-2636. 10.1109/TSP.2003.816886MathSciNetView ArticleGoogle Scholar
  10. Said A, Pearlman WA: A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Transactions on Circuits and Systems for Video Technology 1996,6(3):243-250. 10.1109/76.499834View ArticleGoogle Scholar


© Tanja Karp. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.