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A new algorithm for fast generalized DFTs
[article]

2018
*
arXiv
*
pre-print

We give an

arXiv:1707.00349v3
fatcat:d42p6556orfedhcnzmktnbiogm
*new*arithmetic*algorithm*to compute the*generalized*Discrete Fourier Transform (*DFT*) over finite groups G. ... Our*algorithm*also yields an improved exponent*for*computing the*generalized**DFT*over*general*finite groups G, which beats the longstanding previous best upper bound,*for*any ω. ... We thank the SODA 2018 referees*for*their careful reading of this paper and many useful comments. ...##
###
Implementation of Split Radix Algorithm for 12-Point FFT & IFFT

english

2014
*
International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering
*

english

*A*

*fast*

*algorithm*is proposed

*for*computing

*a*length-N=6 m

*DFT*. The proposed

*algorithm*is

*a*blend of radix-3 and radix-6 FFT. ... KEY WORDS: Discrete Fourier transform (

*DFT*),

*Fast*Fourier transform (FFT), Inverse

*Fast*Fourier transform (IFFT),

*general*split radix, radix 3/6, System Verilog language. ...

*DFT*can be implemented with efficient

*algorithms*

*generally*classified as

*Fast*Fourier transforms (FFT). ...

##
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A fast Fourier transform compiler

1999
*
Proceedings of the ACM SIGPLAN 1999 conference on Programming language design and implementation - PLDI '99
*

*Fast*Fourier Transform Compiler Runtime & Memory Footprint Takes approximately 75 seconds

*for*

*DFT*of size n = 64 to run FFTW

*generated*C code on

*a*200MHz Pentium Pro machine running Linux 2.2 ... performs certain improvements which rely on

*DFT*being

*a*linear transformation genfft "derived" or "discovered"

*new*

*algorithms*, as in case of n = 13 discussed earlier Creation: genfft produces

*a*directed ...

##
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New Decimation-In-Time Fast Hartley Transform Algorithm

2016
*
International Journal of Electrical and Computer Engineering (IJECE)
*

This paper presents

doi:10.11591/ijece.v6i4.10469
fatcat:246vvtfxsjen3bhrova7xh4mri
*a**new**algorithm**for**fast*calculation of the discrete Hartley transform (DHT) based on decimation-in-time (DIT) approach. ... The proposed radix-2^2*fast*Hartley transform (FHT) DIT*algorithm*has*a*regular butterfly structure that provides flexibility of different powers-of-two transform lengths, substantially reducing the arithmetic ... FHT DIT*algorithm*; where , dotted and solid lines stand*for*subtraction and additions respectively IJECE ISSN: 2088-8708 *New*Decimation-in-Time*Fast*Hartley Transform*Algorithm*(Mounir T. ...##
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Automatic Library Generation for Modular Polynomial Multiplication
[article]

2016
*
arXiv
*
pre-print

, using

arXiv:1609.01010v1
fatcat:73syghptxja5tjb5ifmfomv7uu
*new*and existing*algorithms*. ... In this paper we design and implement*algorithms**for*polynomial multiplication using approaches based the*fast*Fourier transform (FFT) and the truncated Fourier transform (TFT). ...*New*transforms can be added by introducing*new*symbols and their definitions, and*new**algorithms*can be*generated*by adding*new*rules. ...##
###
A Flexible Implementation of a Matrix Laurent Series-Based 16-Point Fast Fourier and Hartley Transforms
[article]

2015
*
arXiv
*
pre-print

This paper describes

arXiv:1502.05880v1
fatcat:f7kxhh5qrjaytcrhgwbgqwpmn4
*a*flexible architecture*for*implementing*a**new**fast*computation of the discrete Fourier and Hartley transforms, which is based on*a*matrix Laurent series. ... The hardware structure and synthesis are presented, which handled*a*16-point*fast*transform in 65 nsec, with*a*Xilinx SPARTAN 3E device. ... This paper proposes*a**new**fast**algorithm*and its hardware implementation,*for*computing the discrete Fourier (*DFT*) [4] and Hartley (DHT) [5] transforms of sequences of particular lengths N, namely ...##
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Robust Digital Image Reconstruction via the Discrete Fourier Slice Theorem

2014
*
IEEE Signal Processing Letters
*

We also present methods to

doi:10.1109/lsp.2014.2313341
fatcat:6rk6xr7rijc3dinvr5n64sg6uy
*generate*compact sets of rational projection angles that exactly tile the 2-D*DFT*space. ... The proposed*algorithm*has the same computational complexity as the 2-D*fast*Fourier transform and remains robust to the addition of significant levels of noise. ... In the next section, we present*a**fast**algorithm**for*image reconstruction from noisy Mojette projected views. II. ...##
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Fast Discrete Fourier Spectra Attacks on Stream Ciphers

2011
*
IEEE Transactions on Information Theory
*

We first analyze

doi:10.1109/tit.2011.2158480
fatcat:gcbrjrcunrg6za2xgmgbszgbny
*a*special case of the selective*DFT*method which the previously introduced*algorithm*does not account*for*. ... Consequently, the selective*DFT*attack imposes*a**new*criterion*for*the design of cryptographic strong Boolean functions, which is defined as the spectral immunity of*a*sequence or*a*Boolean function. ... Acknowledgement The authors would like to thank the anonymous referees*for*their valuable and helpful comments. ...##
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Spiral: A Generator for Platform-Adapted Libraries of Signal Processing Alogorithms

2004
*
The international journal of high performance computing applications
*

SPIRAL is

doi:10.1177/1094342004041291
fatcat:tdsp6akylzbeplnnemf42y2eje
*a**generator*of libraries of*fast*software implementations of linear signal processing transforms. ... This paper describes the main components of SPIRAL: the mathematical framework that concisely describes signal transforms and their*fast**algorithms*; the formula*generator*that captures at the*algorithmic*... The space of*algorithms**for**a*given transform is very large, and yet*generated*from*a*small set of rules, which makes possible the automatic*generation*of these*algorithms*, and, furthermore, makes it easy ...##
###
Fast Algorithms for Low-Delay TDAC Filterbanks in MPEG-4 AAC-ELD

2014
*
IEEE/ACM Transactions on Audio Speech and Language Processing
*

In this paper, we present

doi:10.1109/taslp.2014.2346314
fatcat:csuer7f24farxog4bdaueen2xm
*fast**algorithms**for*implementing LD-TDAC filterbanks in AAC-ELD. Two types of*fast**algorithms*are presented. ...*For*filterbanks of lengths 1024 and 960, we also present*a**new**fast*factorization of 15-point DCT-II that requires only 14 irrational multiplications, 3 dyadic rational multiplications and 67 additions ... Since many*fast**algorithms*exist*for*MDCT, this mapping essentially provides*a**fast**algorithm*to implement the*new*filterbanks. ...##
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The FFT: an algorithm the whole family can use

2000
*
Computing in science & engineering (Print)
*

*A*paper by Cooley and Tukey [5] described

*a*recipe

*for*computing Fourier coefficients of

*a*time series that used many fewer machine operations than did the straightforward procedure...What lies over the ... This publication, as well as Garwin's fervent prosletizing, did

*a*lot to help publicize the existence of this (apparently)

*new*

*fast*

*algorithm*. ... Surely the prospect of

*a*huge laborious hand calculation was good motivation

*for*the development of

*a*

*fast*

*algorithm*. ...

##
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A polynomial approach to fast algorithms for discrete Fourier-cosine and Fourier-sine transforms

1991
*
Mathematics of Computation
*

This paper describes

doi:10.1090/s0025-5718-1991-1052103-1
fatcat:uvjfoxzcsrae5mvjk2todllovq
*a**general*method*for*constructing*fast**algorithms**for*the cos-*DFT*, the sin-*DFT*and the DCT, which is based on polynomial arithmetic with Chebyshev polynomials and on the Chinese Remainder ... The discrete Fourier-cosine transform (cos-*DFT*), the discrete Fourier-sine transform (sin-*DFT*) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (*DFT*) of real-valued ... In order to illustrate these*general*considerations, we suggest*a**new*polynomial*algorithm**for*the DCT(3/V). 27^.-/"_,, T2N+j = i< -1)7} -27V7"_, (7 = 1, ... , TV -1), we obtain the following recursive ...##
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A Polynomial Approach to Fast Algorithms for Discrete Fourier-Cosine and Fourier-Sine Transforms

1991
*
Mathematics of Computation
*

This paper describes

doi:10.2307/2008542
fatcat:tbgodn6y4rfafl7m3ewkdbkgbq
*a**general*method*for*constructing*fast**algorithms**for*the cos-*DFT*, the sin-*DFT*and the DCT, which is based on polynomial arithmetic with Chebyshev polynomials and on the Chinese Remainder ... The discrete Fourier-cosine transform (cos-*DFT*), the discrete Fourier-sine transform (sin-*DFT*) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (*DFT*) of real-valued ... In order to illustrate these*general*considerations, we suggest*a**new*polynomial*algorithm**for*the DCT(3/V). 27^.-/"_,, T2N+j = i< -1)7} -27V7"_, (7 = 1, ... , TV -1), we obtain the following recursive ...##
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An efficient multiplierless approximation of the fast Fourier transform using sum-of-powers-of-two (SOPOT) coefficients

2002
*
IEEE Signal Processing Letters
*

*A*treasure of

*fast*

*algorithms*such as the Cooley-Tukey

*fast*Fourier transform (FFT), the prime factor

*algorithm*(PFA) FFT, and the Winogard FFT is available to compute efficiently

*DFT*of different lengths ... ML-FFT

*ALGORITHM*The

*DFT*of

*a*finite-length sequence of length is

*for*(2.1a) where and . ...

##
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A New Relation between "Twiddle Factors" in the Fast Fourier Transformation

2015
*
Elektronika ir Elektrotechnika
*

The

doi:10.5755/j01.eee.21.4.12784
fatcat:zdyogmwnsne4palrr7gyqj2mwe
*fast*Fourier transformation*algorithm*(FFT) probably is the most important*algorithm*in the digital signal processing. ... This paper presents*a**new*relation between "twiddle factors" and gives an optimised form to the existing relations. ... Every*fast**algorithm**for**DFT*is based on the "divide and conquer" idea. ...
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