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Split-radix FFT algorithm
About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.
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TL;DR: Theorems that identify the symmetry in f[x, y] based on the depth of the quadtree to expedite 2-D FFT computation of coherent digital images are presented and applied in transform coding systems and lossy compression of images.
Abstract: The discrete Fourier transform (DFT) of a real sequence f[x, y] of size N/spl times/N, where N=2/sup n/, can be computed by a two-dimensional (2-D) FFT of size N/4, or smaller if f[x, y] is known to have certain symmetries. This paper presents theorems that identify the symmetry in f[x, y] based on the depth of the quadtree to expedite 2-D FFT computation of coherent digital images. In principle, it establishes that if the quadtree of f[x, y] has maximum depth k
5 citations
01 Apr 1981
TL;DR: The DFT computation via the DWT is superior to the fast Fourier transform(FFT) approach in applications where L is relatively small compared with N and where the Walsh and Fourier coefficients are both desired.
Abstract: This paper describes another computational algorithm for the discrete Fourier transform(DFT) via the discrete Walsh transform(DWT). The number of multiplications required by this algorithm is approximately NL/9 where N is the number of data points and L is the number of Fourier coefficients desired. This number shows a 33 % decrease against NL/6 in the previous algorithm published by us. The proposed algorithm can be derived by using conventional sampling points in the DFT. The DFT computation via the DWT is superior to the fast Fourier transform(FFT) approach in applications where L is relatively small compared with N and where the Walsh and Fourier coefficients are both desired.
5 citations
01 Jan 2005
TL;DR: The paper investigates the potential of the very fast Fourier transform (VFFT) for implementation of orthogonal frequency division multiplexing (OFDM) with HiperLAN/2 parameters, and presents a performance comparison with FFT-based OFDM over AWGN channels.
Abstract: The paper investigates the potential of the very fast Fourier transform (VFFT) for implementation of orthogonal frequency division multiplexing (OFDM) with HiperLAN/2 parameters, and presents a performance comparison with FFT-based OFDM over AWGN channels. The VFFT is a fast Fourier transform (FFT) algorithm, which can be implemented in a variety of ways, replacing the FFT either exactly (with floating-point accuracy) or at various levels of approximation. Approximate forms with lower complexity reduce computational load and system complexity, and lead to the VFFT-based OFDM (G-OFDM and % n G-OFDM). n G-OFDM with different values of n-quantisation level trades system complexity against system performance. (6 pages)
5 citations
Journal Article•
5 citations
11 Jun 1991
TL;DR: A fast algorithm for computing the two-dimensional discrete cosine transform (2-D DCT) is proposed which produces a regular structure which makes it attractive for VLSI implementation.
Abstract: A fast algorithm for computing the two-dimensional discrete cosine transform (2-D DCT) is proposed. In this algorithm the 2-D DCT is converted into a form of 2-D DFT (discrete Fourier transform) which is called the odd DFT. The odd DFT can be calculated by a DFT followed by post-multiplications. The DFT part of the odd DFT is calculated by the fast discrete Radon transform. The complexity of the proposed algorithm is comparable to that of the polynomial transform approach. This new algorithm produces a regular structure which makes it attractive for VLSI implementation. Furthermore, the computation can be performed in parallel. >
5 citations