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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: A new GPS signal acquisition method based on decomposition of FFT is proposed to improve the acquisition performance and is implemented, validated and compared with conventional serial search and radix2 FFT search algorithms using Intermediate Frequency GPS signal.
10 citations
01 Jan 2006
TL;DR: These test results demonstrate that good algorithms and codes, accurate performance evaluation models, and effective search methods, combined together provide a system framework (library) to derive automatically fast FFT implementations.
Abstract: This thesis considers systematic methodologies for finding optimized implementations for the fast Fourier transform (FFT). By employing rewrite rules (e.g., the CooleyTukey formula), we obtain a divide and conquer procedure (decomposition) that breaks down the initial transform into combinations of different smaller size sub-transforms, which are graphically represented as breakdown trees. Recursive application of the rewrite rules generates a set of algorithms and alternative codes for the FFT computation. The set of "all" possible implementations (within the given set of the rules) results in pairing the possible breakdown trees with the code implementation alternatives. To evaluate the quality of these implementations, we develop analytical and experimental performance models. Based on these models, we derive methods dynamic programming, soft decision dynamic programming and exhaustive search to find the implementation with minimal runtime. Our test results demonstrate that good algorithms and codes, accurate performance evaluation models, and effective search methods, combined together provide a system framework (library) to derive automatically fast FFT implementations.
10 citations
TL;DR: The decomposition of the FFT algorithm into the basic Butterfly operations is described, as this allows the algorithm to be fully implemented by the successive coherent addition and subtraction of two wavefronts, facilitating a simple and robust hardware implementation based on waveguided hybrid devices as employed in coherent optical detection modules.
Abstract: Optical structures to implement the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms for discretely sampled data sets are considered. In particular, the decomposition of the FFT algorithm into the basic Butterfly operations is described, as this allows the algorithm to be fully implemented by the successive coherent addition and subtraction of two wavefronts (the subtraction being performed after one has been appropriately phase shifted), so facilitating a simple and robust hardware implementation based on waveguided hybrid devices as employed in coherent optical detection modules. Further, a comparison is made to the optical structures proposed for the optical implementation of the quantum Fourier transform and they are shown to be very similar.
10 citations
TL;DR: For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably by performing the cyclic convolution with the Mersenne prime number-theoretic transform developed originally by Rader.
Abstract: In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplisbed by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.
10 citations
TL;DR: The focus is on studying the analog of the Cooley-Tukey algorithm because the number of operations applied to calculate the n-dimensional FFT is considerably less than in the conventional algorithm.
Abstract: The one-dimensional fast Fourier transform (FFT) is the most popular tool for calculating the multidimensional Fourier transform. As a rule, to estimate the n-dimensional FFT, a standard method of combining one-dimensional FFTs, the so-called "by rows and columns" algorithm, is used in the literature. For fast calculations, different researchers try to use parallel calculation tools, the most successful of which are searches for the algorithms related to the computing device architecture: cluster, video card, GPU, etc. [1, 2]. The possibility of paralleling another algorithm for FFT calculation, which is an n-dimensional analog of the Cooley-Tukey algorithm [3, 4], is studied in this paper. The focus is on studying the analog of the Cooley-Tukey algorithm because the number of operations applied to calculate the n-dimensional FFT is considerably less than in the conventional algorithm nN n log2 N of addition operations and 1/2N n + 1log2 N of multiplication operations of addition operations and $$\frac{{2^n - 1}} {{2^n }}N^n \log _2 N$$ of multiplication operations against: N n + 1log2 N of addition operations and 1/2N n + 1log2 N of in combining one-dimensional FFTs.
10 citations