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Fast Computation of Discrete Fourier Transforms Using Polynomial Transfwms
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TLDR
This paper presents two methods for computing discrete Fourier transforms (DFT) by polynomial transforms and shows that these techniques are particularly well adapted to multidimensional DFTs as well as to some one-dimensional DFT's and yield algorithms that are, in many instances, more efficient than the fast Fourier transform (FFT) or the Winograd Fourier Transform (WFTA).About:
The article was published on 1979-01-01 and is currently open access. It has received 64 citations till now. The article focuses on the topics: Discrete Fourier series & Discrete Fourier transform.read more
Citations
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Fast Fourier transforms: a tutorial review and a state of the art
Pierre Duhamel,Martin Vetterli +1 more
TL;DR: MadMadisetti, D. B. Williams, Eds. as discussed by the authors, LCAV-2005-009 Record created on 2005-06-27, modified on 2017-05-12
Journal ArticleDOI
Image algebra techniques for parallel image processing
Gerhard X. Ritter,Paul D. Gader +1 more
TL;DR: This paper shows how the image algebra suggests a general-purpose cellular pyramid array processor for real time image processing tasks and demonstrates how algebraic techniques can be used to develop systematic methods for deriving parallel algorithms.
Journal ArticleDOI
Algebraic Signal Processing Theory: Foundation and 1-D Time
Markus Püschel,Jose M. F. Moura +1 more
TL;DR: The paper illustrates the general ASP theory with the standard time shift, presenting a unique signal model for infinite time and several signal models for finite time and the latter models illustrate the role played by boundary conditions and recover the discrete Fourier transform and its variants as associated Fourier transforms.
Book
Fast Algorithms for Signal Processing
TL;DR: A collection of cyclic convolution algorithms and a collection of Winograd small FFT algorithms for solving Toeplitz systems are presented.
Proceedings ArticleDOI
Polynomial transform computation of the 2-D DCT
TL;DR: A 2-D DCT (discrete cosine transform) algorithm based on a direct polynomial approach is presented and it is shown that, although being mathematically involved, it possesses a clean, butterfly-based structure.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
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Discrete Fourier transforms when the number of data samples is prime
TL;DR: The discrete Fourier transform of a sequence of N points, where N is a prime number, is shown to be essentially a circular correlation, which permits the discrete Fouriers transform to be computed by means of a fast Fouriertransform algorithm, with the associated increase in speed, even though N is prime.
Book
Introduction to Number Theory
TL;DR: A specific feature of this text on number theory is the rather extensive treatment of Diophantine equations of second or higher degree as discussed by the authors, and a large number of non-routine problems are given.
Journal ArticleDOI
Introduction to Number Theory. By T. Nagell. Second Edition. Pp. 309. $5.50. 1964. (Chelsea.)
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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.