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

Taizo Suzuki, Seisuke Kyochi, Yuichi Tanaka, Masaaki Ikehara

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This paper presents M-channel (M= 2 N, N∈ N, N≥ 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.

Original languageEnglish
Pages (from-to)99-118
Number of pages20
JournalMultidimensional Systems and Signal Processing
Issue number1
Publication statusPublished - 2018 Jan 1

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Information Systems
  • Hardware and Architecture
  • Computer Science Applications
  • Artificial Intelligence
  • Applied Mathematics


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