Topic
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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Patent•
14 Sep 1987TL;DR: In this article, a fast Fourier transform circuit, including an illustrative radix-eight DFT kernel that operates on an n-bit-serial data format, for an efficient serial-like, pipelined operation within the DFT.
Abstract: A fast Fourier transform circuit, including an illustrative radix-eight discrete Fourier transform (DFT) kernel that operates on an n-bit-serial data format, for an efficient serial-like, pipelined operation within the DFT. The circuit performs a four-point DFT on half of the input data words at a time, stores intermediate results from the four-point DFT in a commutation stage, then combines the intermediate results in two two-point DFTs. Internal multiplication in the eight-point DFT is effected in delay registers that also serve to store the intermediate results, thereby providing an economy of timing and circuit routing. Interleaving and deinterleaving operations convert the data format between three-bit-serial and conventional bit-parallel used outside the eight-point DFT kernel, which may therefore be easily cascaded for more complex FFT operations. The DFT kernel also includes means for selectively bypassing butterfly computation modules to perform shorter-length DFTs.
30 citations
Patent•
04 Apr 2007TL;DR: In this paper, the authors described techniques for performing Fast Fourier Transform (FFT) using a delayless pipeline and an Inverse FFT (IFFT) using the main memory.
Abstract: Techniques for performing Fast Fourier Transforms (FFT) are described. In some aspects, calculating the Fast Fourier Transform is achieved with an apparatus having a memory (610), a Fast Fourier Transform engine (FFTe) having one or more registers (650) and a delayless pipeline (630), the FFTe configured to receive a multi-point input from the main memory (610), store the received input in at least one of the one or more registers (650), and compute either or both of a Fast Fourier Transform (FFT) and an Inverse Fast Fourier Transform (IFFT) on the input using the delayless pipeline.
30 citations
19 Mar 1984
TL;DR: This paper presents an in-place, radix-2 FFT that does the unscrambling while the FFT is being calculated rather than as a separate process.
Abstract: Most Cooley-Tukey, in-place Fast Fourier Transform (FFT) algorithms result in the output being permuted or scrambled in order. For a radix-2 FFT, this order can be easily found by reversing the order of the bits of the address, and the unscrambler is called a bit-reversed counter. In some machines, this unscrambling takes from 10% to 50% of the total execution time. This paper presents an in-place, radix-2 FFT that does the unscrambling while the FFT is being calculated rather than as a separate process. The theoretical framework is based on index maps [1] and ideas used on the in-place, in-order prime factor FFT (PFA) [2]. The non-scrambled algorithm is implemented in FORTRAN. The size of the program is essentially the same as the regular radix-2 FFT with its bit-reversed counter.
29 citations
TL;DR: A Fast Fourier Transform algorithm is described which is especially suited for structural dynamics which incorporates several features selected from many variations of the original Cooley and Tukey1 algorithm with the goal of making the most efficient use of computer time and storage while maintaining simplicity.
Abstract: A Fast Fourier Transform algorithm (FFT) is described which is especially suited for structural dynamics. The routine incorporates several features selected from many variations of the original Cooley and Tukey1 algorithm with the goal of making the most efficient use of computer time and storage while maintaining simplicity. Some introductory material to Fourier transform techniques and a description of the original algorithm are also included. In addition, the source listing of the subroutine FFT is reproduced.
29 citations
TL;DR: It is shown that the QS‐PCFFT maintains high‐order convergence and scales as O(N) in memory and O( N log N) in floating point operations.
Abstract: In this paper, a novel fast, high-order solution procedure referred to as the quadrature sampled pre-corrected fast-Fourier transform (QS-PCFFT) is presented. The method accelerates far-interaction terms of an integral operator using the discontinuous FFT 1, which combines Gaussian-quadrature integration with the FFT. This method is applied to the locally corrected Nystrom solution of electromagnetic scattering problems. It is shown that the QS-PCFFT maintains high-order convergence and scales as O(N) in memory and O(N log N) in floating point operations. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 343–349, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10760
29 citations