Multidimensional Systems and Signal Processing

, Volume 29, Issue 1, pp 99–118 | Cite as

Multiplierless lifting-based fast X transforms derived from fast Hartley transform factorization

  • Taizo Suzuki
  • Seisuke Kyochi
  • Yuichi Tanaka
  • Masaaki Ikehara


This paper presents M-channel (\(M=2^{N}\), \(N\in \mathbb {N}\), \(N\ge 1\)) multiplierless lifting-based (ML-) fast X transforms (FXTs), where X \(=\) F (Fourier), C (cosine), S (sine), and H (Hartley), i.e., FFT, FCT, FST, and FHT, derived from FHT factorization as way of lowering the cost of signal (image) processing. The basic forms of ML-FXTs are described. Then, they are customized for efficient image processing. The customized ML-FFT has a real-valued calculation followed by a complex-valued one. The ML-FCT customization for a block size of 8, which is a typical size for image coding, further reduces computational costs. We produce two customized ML-FCTs for lossy and lossless image coding. Numerical simulations show that ML-FFT and ML-FCTs perform comparably to the conventional methods in spite of having fewer operations.



The authors would like to thank the anonymous reviewers, Dr. H. Aso, and Dr. K. Sugimoto for providing many constructive suggestions that significantly improve the presentation of this paper. This work was supported by a JSPS Grant-in-Aid for Young Scientists (B), Grant Number 16K18100.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Taizo Suzuki
    • 1
  • Seisuke Kyochi
    • 2
  • Yuichi Tanaka
    • 3
  • Masaaki Ikehara
    • 4
  1. 1.Faculty of Engineering, Information and SystemsUniversity of TsukubaTsukubaJapan
  2. 2.Department of Information and Media EngineeringThe University of KitakyushuKitakyushuJapan
  3. 3.Graduate School of BASETokyo University of Agriculture and TechnologyKoganeiJapan
  4. 4.Department of Electronics and Electrical EngineeringKeio UniversityYokohamaJapan

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