scispace - formally typeset
Search or ask a question
Topic

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
More filters
Proceedings Article
01 Jan 1991

23 citations

Journal ArticleDOI
TL;DR: A method for converting any nesting DFT algorithm to the type-I discrete W transform (DWT-I) is introduced and is more efficient that either WFTA or PFA for large N, and it is more flexible for the choice of transform length.
Abstract: A method for converting any nesting DFT algorithm to the type-I discrete W transform (DWT-I) is introduced. A nesting algorithm that differs from either the Windograd Fourier transform algorithm (WFTA) or the prime factor FFT algorithm (PFA) is presented. New small-N DETs, which are suitable for this nesting algorithm, are developed based on using sparse matrix decomposition. The proposed algorithm is more efficient that either WFTA or PFA for large N, and it is more flexible for the choice of transform length, because 32 points are used. For 2D processing, the proposed algorithm is more efficient than the polynomial transform. >

23 citations

Patent
21 Oct 1991
TL;DR: In this paper, a radix-12 FFT is presented, where complex data are represented in a 1, W 3 coordinate system rather than in a classic 1,j coordinate system, and the only multiplicative scaler in the complex twiddle factors is the reciprocal of the square root of 3 which appears six times and which by conversion to canonical signed digit code, can be accurately expressed by 5 adds.
Abstract: Using classic Fast Fourier Transform (FFT) rules, a radix-12 FFT is composed of a first tier of 2 multiplierless radix-6 transformers followed by multiplierless radix-2 transformers, or by its transpose configuration. Complex data are represented in a 1, W 3 coordinate system rather than in a classic 1,j coordinate system. The only multiplicative scaler in the complex twiddle factors is the reciprocal of the square root of 3 which appears six times and which by conversion to canonical signed digit code, can be accurately expressed by 5 adds. As a consequence the complex twiddle factor multipliers and ancillary address reduce to a total of 144 real adds required to perform the entire complex 12-point FFT.

23 citations

Book ChapterDOI
TL;DR: The tangent FFT is presented, a straightforward in-place cache-friendly DFT algorithm having exactly the same operation counts as Van Buskirk's algorithm, and it is pinpoints how the tangentFFT saves time compared to the split-radix FFT.
Abstract: The split-radix FFT computes a size-n complex DFT, when n is a large power of 2, using just 4n lg n-6n+8 arithmetic operations on real numbers. This operation count was first announced in 1968, stood unchallenged for more than thirty years, and was widely believed to be best possible. Recently James Van Buskirk posted software demonstrating that the split-radix FFT is not optimal. Van Buskirk's software computes a size-n complex DFT using only (34/9 + o(1))n lg n arithmetic operations on real numbers. There are now three papers attempting to explain the improvement from 4 to 34/9: Johnson and Frigo, IEEE Transactions on Signal Processing, 2007; Lundy and Van Buskirk, Computing, 2007; and this paper. This paper presents the "tangent FFT," a straightforward in-place cache-friendly DFT algorithm having exactly the same operation counts as Van Buskirk's algorithm. This paper expresses the tangent FFT as a sequence of standard polynomial operations, and pinpoints how the tangent FFT saves time compared to the split-radix FFT. This description is helpful not only for understanding and analyzing Van Buskirk's improvement but also for minimizing the memory-access costs of the FFT.

23 citations

Proceedings ArticleDOI
15 Apr 2002
TL;DR: A novel twiddle factor-based FFT algorithm to reduce the frequency of memory access as well as multiplication operations is presented and shows that, for a 32-point FFT, the new algorithm leads to as much as 20% reduction in clock cycles and an average of 30% reduced in memory access than that of the conventional DIF FFT.
Abstract: In microprocessor-based systems, memory access is expensive due to longer latency and higher power consumption. In this paper, we present a novel FFT algorithm to reduce the frequency of memory access as well as multiplication operations. For an N-point FFT, we design the FFT with two distinct sections: (1) The first section of the FFT structure computes the butterflies involving twiddle factors WNj (j ≠ 0) through a computation/partitioning scheme similar to the Hoffman coding. In this section, all the butterflies sharing the same twiddle factor will be clustered and computed together. In this way, redundant memory access to load twiddle factors is avoided. (2) In the second section, the remaining (N - 1) butterflies involving the twiddle factor WN0 are computed with a register-based breadth first tree traversal algorithm. This novel twiddle factor-based FFT is tested on the TIT MS320C62x digital signal processor. The results show that, for a 32-point FFT, the new algorithm leads to as much as 20% reduction in clock cycles and an average of 30% reduction in memory access than that of the conventional DIF FFT.

23 citations


Network Information
Related Topics (5)
Wavelet
78K papers, 1.3M citations
81% related
Robustness (computer science)
94.7K papers, 1.6M citations
78% related
Feature extraction
111.8K papers, 2.1M citations
77% related
Support vector machine
73.6K papers, 1.7M citations
76% related
Optimization problem
96.4K papers, 2.1M citations
76% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
202224
20211
20188
201757
201692