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Prime-factor FFT algorithm
About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.
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TL;DR: A structure theorem is devised to construct systematically various vector-radix decimation-in-frequency FFT algorithms from their 1-D counterparts.
Abstract: A general form of the matrix representation for multidimensional, vector-radix, fast Fourier transform (FFT) algorithms using decimation-in-frequency is presented. A structure theorem is devised to construct systematically various vector-radix decimation-in-frequency FFT algorithms from their 1-D counterparts. Logic diagrams are provided to facilitate the software and hardware implementation of the algorithms. The computational complexity of several of the algorithms is considered. >
28 citations
01 Oct 1997
TL;DR: The authors propose one-dimensional and two-dimensional systolic architectures for the discrete Hilbert transform that have the features of massive parallelism, high pipelining, regular data flow, modular nature and local interconnections.
Abstract: A new fast parallel array algorithm to compute the discrete Hilbert transform for radix-2 length sequences is proposed. Unlike the existing fast methods which use transforms such as the fast Fourier transform, the proposed algorithm does not require the help of any fast transforms. This array algorithm offers a suitable expression for developing a VLSI systolic array for the discrete Hilbert transform. The authors propose one-dimensional and two-dimensional systolic architectures for the discrete Hilbert transform. The proposed architectures have the features of massive parallelism, high pipelining, regular data flow, modular nature and local interconnections. These arrays offer high speed computation of the discrete Hilbert transform for real-time signal processing applications.
28 citations
TL;DR: In this work the generalized discrete Fourier transform (GFT), which includes the DFT as a particular case, is considered, and two pairs of fast algorithms for evaluating a multidimensional GFT are given (T-algorithm, F-al algorithm, and T′-algorithms, F′-Algorithm).
Abstract: In this work the generalized discrete Fourier transform (GFT), which includes the DFT as a particular case, is considered. Two pairs of fast algorithms for evaluating a multidimensional GFT are given (T-algorithm, F-algorithm, and T′-algorithm, F′-algorithm). It is shown that in the case of the DFT of a vector, the T-algorithm represents a form of the classical FFT algorithm based on a decimation in time, and the F-algorithm represents a form of the classical FFT algorithm based on decimation in frequency. Moreover, it is shown that the T′-algorithm and the T-algorithm involve exactly the same arithmetic operations on the same data. The same property holds for the F′-algorithm and the F-algorithm. The relevance of such algorithms is discussed, and it is shown that the T′-algorithm and the F′-algorithm are particularly advantageous for evaluating the DFT of large sets of data.
28 citations
TL;DR: An efficient iterative version of the FFT algorithm performs as a first step a bit-reversal permutation of the input list that swaps elements whose indices have binary representations that are the reverse of each other.
Abstract: One well known algorithm is the Fast Fourier Transform (FFT). An efficient iterative version of the FFT algorithm performs as a first step a bit-reversal permutation of the input list. The bit-reversal permutation swaps elements whose indices have binary representations that are the reverse of each other. Using an amortized approach, this operation can be made to run in linear time on a random-access machine. An intriguing question is whether a linear-time implementation is also feasible on a pointer machine, that is, in a purely functional setting. We show that the answer to this question is in the affirmative. In deriving a solution, we employ several advanced programming language concepts such as nested datatypes, associated fold and unfold operators, rank-2 types and polymorphic recursion.
28 citations
TL;DR: An error propagation model is proposed for the in-place decimation-in-time version of the radix-2 FFT algorithm and an accurate error expression and error variance for the computation of FFT are derived.
Abstract: An error propagation model is proposed for the in-place decimation-in-time version of the radix-2 FFT algorithm. With the model, an accurate error expression and error variance for the computation of FFT are derived. This correspondence deals with fixed-point and block floating-point arithmetic. Simulation results agree closely with the theoretical predicted ones. We find that some roundoff errors at different stages correlate with each other. The density of correlations is closely associated with the round-off approach used in butterfly calculations.
28 citations