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

Taizo Suzuki, Seisuke Kyochi, Yuichi Tanaka, Masaaki Ikehara

    Research output: Contribution to journalArticle


    This paper presents M-channel ((Formula presented.), (Formula presented.), (Formula presented.)) multiplierless lifting-based (ML-) fast X transforms (FXTs), where X (Formula presented.) 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)1-20
    Number of pages20
    JournalMultidimensional Systems and Signal Processing
    Publication statusAccepted/In press - 2016 Sep 24

    ASJC Scopus subject areas

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

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