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Multiplierless lifting-based fast X transforms derived from fast Hartley transform factorization. (English) Zbl 1450.94023
Summary: 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.
MSC:
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
65T50 Numerical methods for discrete and fast Fourier transforms
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