Proceedings ArticleDOI
The design of optimal DFT algorithms using dynamic programming
H. Johnson,C.S. Burrus +1 more
- Vol. 7, pp 20-23
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TLDR
A highly effective dynamic programming algorithm is presented as a solution to the problem of finding an algorithm from this class which is optimal with respect to the specific add, multiply, and data transfer characteristics of a partlcular implementation.Abstract:
A broad class of efficient, discrete Fourier transform algorithms is developed by partitioning short DFT algorithms into factors. The factored short DFT's are combined into longer DFT's using a prime factor algorithm (PFA). By exploiting a property which allows some of the factors to commute, a large set of possible DFT algorithms is generated which contains both the prime factor algorithm and the Winograd Fourier Transform Algorithm (WFTA) as special cases. The problem of finding an algorithm from this class which is optimal with respect to the specific add, multiply, and data transfer characteristics of a partlcular implementation is posed, and a highly effective dynamic programming algorithm is presented as a solution.read more
Citations
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Proceedings ArticleDOI
FFTW: an adaptive software architecture for the FFT
Matteo Frigo,Steven G. Johnson +1 more
TL;DR: An adaptive FFT program that tunes the computation automatically for any particular hardware, and tests show that FFTW's self-optimizing approach usually yields significantly better performance than all other publicly available software.
Proceedings ArticleDOI
A fast Fourier transform compiler
TL;DR: The internals of this special-purpose compiler, called genfft, are described in some detail, and it is argued that a specialized compiler is a valuable tool.
Journal ArticleDOI
Spiral: A Generator for Platform-Adapted Libraries of Signal Processing Algorithms
Markus Püschel,Jose M. F. Moura,Bryan Singer,Jianxin Xiong,Jeremy Johnson,David Padua,Manuela Veloso,Robert W. Johnson +7 more
TL;DR: The main components of SPIRAL are described: the mathematical framework that concisely describes signal transforms and their fast algorithms; the formula generator that captures at the algorithmic level the degrees of freedom in expressing a particular signal processing transform; a formula translator that encapsulates the compilation degrees offreedom when translating a specific algorithm into an actual code implementation.
Book ChapterDOI
Fast Fourier Transforms
TL;DR: In this paper, the authors discuss the controversial claim that any continuous periodic signal could be represented by the sum of properly chosen sinusoidal waves, and discuss the use of the Fourier transform for digital signal processing.
Peer Review
Multidigit multiplication for mathematicians
TL;DR: In this article , a survey of techniques for multiplying elements of various commutative rings is presented, including dual Karatsuba multiplication, dual Toom multiplication and dual FFT.
References
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Book
Dynamic Programming
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Journal ArticleDOI
A prime factor FFT algorithm using high-speed convolution
TL;DR: Two recently developed ideas, the conversion of a discrete Fourier transform to convolution and the implementation of short convolutions with a minimum of multiplications, are combined to give efficient algorithms for long transforms.
Journal ArticleDOI
On computing the Discrete Fourier Transform.
TL;DR: New algorithms for computing the Discrete Fourier Transform of n points use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions.