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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27 Apr 1993TL;DR: An algorithm for fast adaptive filtering that applies a FFT (fast Fourier transform)-based iterative method and uses sliding data windows involving block updating and downdating computations and computes the tap weight filter vector in O(L log N) operations.
Abstract: An algorithm for fast adaptive filtering is proposed. The algorithm applies a FFT (fast Fourier transform)-based iterative method and uses sliding data windows involving block updating and downdating computations. The method is stable and robust, and computes the tap weight filter vector in O(L log N) operations, where the sliding window Toeplitz data matrix X is L-by-N. The complexity thus generally lies between those of the family of unstable but fast, O(N), methods and the stable but slow O(N/sup 2/) Cholesky factor updating methods. >
14 citations
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TL;DR: An efficient algorithm (involving real arithmetic only) for N-point DFT is developed and used as the basic building block for developing the real valued fast Fourier transform (FFT).
Abstract: The authors earlier developed a fast recursive algorithm for the discrete sine transform (see IEEE Trans. Acoust. Speech Signal Process., vol.38, no.3, p.553-7, 1990). This algorithm is used as the basic building block for developing the real valued fast Fourier transform (FFT). It is assumed that the input sequence is real and of length N, an integer power of 2. The N-point discrete Fourier transform (DFT) of a real sequence can be implemented via the real (cos DFT) and imaginary (sin DFT) components. The N-point cos DFT in turn can be developed from N/2-point cos DFT and N/4-point discrete sine transform (DST). Similarly, the N-point sin DFT can be developed from N2-point sin DFT and N/4-point DST. Using this approach, an efficient algorithm (involving real arithmetic only) for N-point DFT is developed. >
14 citations
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01 Aug 1997TL;DR: A new pruning method for an FFT type of transform structure is proposed, whose novelty lies in the fact that it is able to complete a previously pruned transform or to progress from one level of pruning to another.
Abstract: A new pruning method for an FFT type of transform structure is proposed. Its novelty lies in the fact that, besides being able to prune the transform, it is able to complete a previously pruned transform or to progress from one level of pruning to another. The method can be directly applied to fast progressive image coding.
14 citations
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TL;DR: An algorithm is proposed for computing the Fourier Transform (FT) of a uniformly sampled signal at arbitrary frequencies and its computational aspects and its error behavior with typical signals have been critically examined.
Abstract: An algorithm is proposed for computing the Fourier Transform (FT) of a uniformly sampled signal at arbitrary frequencies. In most of the applications, the algorithm retains the computational efficiency of the Fast Fourier Transform (FFT) algorithm. The method is based on the fact that the FT at an arbitrary frequency can be expressed as a weighted sum of its Discrete Fourier Transform (DFT) coefficients. In the proposed method, these weights are suitably approximated so that the desired FT is very nearly the sum of (i) a few dominant terms of the sum of the DFT which are computed directly, and (ii) the DFT of a new sequence obtained by multiplying the original sequence with a sawtooth function. The number of directly computed terms is so chosen that the error of approximation does not exceed the specified limits. The computational aspects of the algorithm and its error behavior with typical signals have been critically examined.
14 citations
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TL;DR: A simple modification of the FFT algorithm that results in an efficient method for calculating the transform only at evenly spaced frequencies on a logarithmic scale is proposed.
Abstract: A standard fast Fourier transform (FFT) computes the transform at evenly spaced points on a linear scale. A simple modification of the FFT algorithm that results in an efficient method for calculating the transform only at evenly spaced frequencies on a logarithmic scale is proposed. The saving in the number of operations, compared with a standard FFT, is approximately 60% for typical values. >
14 citations