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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.


Papers
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Journal ArticleDOI
TL;DR: This brief presents a new type of fast Fourier transform (FFT) hardware architectures called serial commutator (SC) FFT, based on the observation that, in the radix-2 FFT algorithm, only half of the samples at each stage must be rotated.
Abstract: This brief presents a new type of fast Fourier transform (FFT) hardware architectures called serial commutator (SC) FFT. The SC FFT is characterized by the use of circuits for bit-dimension permutation of serial data. The proposed architectures are based on the observation that, in the radix-2 FFT algorithm, only half of the samples at each stage must be rotated. This fact, together with a proper data management, makes it possible to allocate rotations only every other clock cycle. This allows for simplifying the rotator, halving the complexity with respect to conventional serial FFT architectures. Likewise, the proposed approach halves the number of adders in the butterflies with respect to previous architectures. As a result, the proposed architectures use the minimum number of adders, rotators, and memory that are necessary for a pipelined FFT of serial data, with 100% utilization ratio.

33 citations

Journal ArticleDOI
TL;DR: A memory efficient approximation to the nonuniform Fourier transform of a support limited sequence is derived based on the theory of shift-invariant representations and an exact expression for the worst-case mean square approximation error is derived.
Abstract: The main focus of this paper is to derive a memory efficient approximation to the nonuniform Fourier transform of a support limited sequence. We show that the standard nonuniform fast Fourier transform (NUFFT) scheme is a shift invariant approximation of the exact Fourier transform. Based on the theory of shift-invariant representations, we derive an exact expression for the worst-case mean square approximation error. Using this metric, we evaluate the optimal scale-factors and the interpolator that provides the least approximation error. We also derive the upper-bound for the error component due to the lookup tablebased evaluation of the interpolator; we use this metric to ensure that this component is not the dominant one. Theoretical and experimental comparisons with standard NUFFT schemes clearly demonstrate the significant improvement in accuracy over conventional schemes, especially when the size of the uniform fast Fourier transform (FFT) is small. Since the memory requirement of the algorithm is dependent on the size of the uniform FFT, the proposed developments can lead to iterative signal reconstruction algorithms with significantly lower memory demands.

33 citations

Patent
20 Aug 1974
TL;DR: In this article, two parallel shift registers store and shift the real and imaginary components of the complex number X k + iY k, successively shifted one bit per strobe in response to receipt of new data.
Abstract: A wholly digital system for computing the discrete Fourier transform of sequentially received data in a recursive fashion. Two parallel shift registers store and shift the real and imaginary components of the complex number X k + iY k . The data in the parallel registers are successively shifted one bit per strobe in response to receipt of new data. Additional logic operates recursively on successive data inputs to compute the discrete Fourier transform.

33 citations

Proceedings ArticleDOI
06 Mar 2014
TL;DR: A new algorithm called the sparse FFT (sFFT) can compute the Fourier transform more efficiently than traditional FFTs for sparse signals like spectrum sensing, radar signal processing, and pattern matching.
Abstract: Applications like spectrum sensing, radar signal processing, and pattern matching by convolving a signal with a long code, as in GPS, require large FFT sizes. ASIC implementations of such FFTs are challenging due to their large silicon area and high power consumption. However, the signals in these applications are sparse, i.e., the energy at the output of the FFT/IFFT is concentrated at a limited number of frequencies and with zero/negligible energy at most frequencies. Recent advances in signal processing have shown that, for such sparse signals, a new algorithm called the sparse FFT (sFFT) can compute the Fourier transform more efficiently than traditional FFTs [1].

33 citations

Journal ArticleDOI
TL;DR: A general class of split-radix fast Fourier transform (FFT) algorithms for computing the length-2m DFT is proposed by introducing a new recursive approach coupled with an efficient method for combining the twiddle factors and it is shown that the number of arithmetic operations required is independent of s and is (2m-3)2m+1+8.
Abstract: In this paper, a general class of split-radix fast Fourier transform (FFT) algorithms for computing the length-2m DFT is proposed by introducing a new recursive approach coupled with an efficient method for combining the twiddle factors. This enables the development of higher split-radix FFT algorithms from lower split-radix FFT algorithms without any increase in the arithmetic complexity. Specifically, an arbitrary radix-2/2s FFT algorithm for any value of s, 4les sles m, is proposed and its arithmetic complexity analyzed. It is shown that the number of arithmetic operations (multiplications plus additions) required by the proposed radix-2/2s FFT algorithm is independent of s and is (2m-3)2m+1+8 regardless of whether a complex multiplication is carried out using four multiplications and two additions or three multiplications and three additions. This paper thus provides a variety of choices and ways for computing the length-2m DFT with the same arithmetic complexity.

33 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
202224
20211
20188
201757
201692