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A new algorithm for fast generalized DFTs [article]

Chloe Ching-Yun Hsu, Chris Umans
2018 arXiv   pre-print
We give an 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.  ... 
arXiv:1707.00349v3 fatcat:d42p6556orfedhcnzmktnbiogm

Implementation of Split Radix Algorithm for 12-Point FFT & IFFT
english

P.MALYA DRI, D.JAYANA YUDU, G.MAHEN DRA
2014 International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering  
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).  ... 
doi:10.15662/ijareeie.2014.0310040 fatcat:lhoq7groavcabbmcw7ka2tzote

A fast Fourier transform compiler

Matteo Frigo
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  ... 
doi:10.1145/301618.301661 dblp:conf/pldi/Frigo99 fatcat:vmlhh4vuyravrnsq5rz3shdlmm

New Decimation-In-Time Fast Hartley Transform Algorithm

Mounir Taha Hamood
2016 International Journal of Electrical and Computer Engineering (IJECE)  
This paper presents 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.  ... 
doi:10.11591/ijece.v6i4.10469 fatcat:246vvtfxsjen3bhrova7xh4mri

Automatic Library Generation for Modular Polynomial Multiplication [article]

Lingchuan Meng
2016 arXiv   pre-print
, using 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.  ... 
arXiv:1609.01010v1 fatcat:73syghptxja5tjb5ifmfomv7uu

A Flexible Implementation of a Matrix Laurent Series-Based 16-Point Fast Fourier and Hartley Transforms [article]

R.C. de Oliveira, H.M. de Oliveira, R.M. Campello de Souza, E.J.P. Santos
2015 arXiv   pre-print
This paper describes 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  ... 
arXiv:1502.05880v1 fatcat:f7kxhh5qrjaytcrhgwbgqwpmn4

Robust Digital Image Reconstruction via the Discrete Fourier Slice Theorem

Shekhar S. Chandra, Nicolas Normand, Andrew Kingston, Jeanpierre Guedon, Imants Svalbe
2014 IEEE Signal Processing Letters  
We also present methods to 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.  ... 
doi:10.1109/lsp.2014.2313341 fatcat:6rk6xr7rijc3dinvr5n64sg6uy

Fast Discrete Fourier Spectra Attacks on Stream Ciphers

Guang Gong, Sondre Ronjom, Tor Helleseth, Honggang Hu
2011 IEEE Transactions on Information Theory  
We first analyze 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.  ... 
doi:10.1109/tit.2011.2158480 fatcat:gcbrjrcunrg6za2xgmgbszgbny

Spiral: A Generator for Platform-Adapted Libraries of Signal Processing Alogorithms

Markus Püschel, José M. F. Moura, Bryan Singer, Jianxin Xiong, Jeremy Johnson, David Padua, Manuela Veloso, Robert W. Johnson
2004 The international journal of high performance computing applications  
SPIRAL is 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  ... 
doi:10.1177/1094342004041291 fatcat:tdsp6akylzbeplnnemf42y2eje

Fast Algorithms for Low-Delay TDAC Filterbanks in MPEG-4 AAC-ELD

Ravi K. Chivukula, Yuriy A. Reznik, Yanyan Hu, Venkat Devarajan, Mythreya Jayendra-Lakshman
2014 IEEE/ACM Transactions on Audio Speech and Language Processing  
In this paper, we present 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.  ... 
doi:10.1109/taslp.2014.2346314 fatcat:csuer7f24farxog4bdaueen2xm

The FFT: an algorithm the whole family can use

D.N. Rockmore
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.  ... 
doi:10.1109/5992.814659 fatcat:c4gmmbcvrfh4vi4ybdmbtybfm4

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

G. Steidl, M. Tasche
1991 Mathematics of Computation  
This paper describes 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  ... 
doi:10.1090/s0025-5718-1991-1052103-1 fatcat:uvjfoxzcsrae5mvjk2todllovq

A Polynomial Approach to Fast Algorithms for Discrete Fourier-Cosine and Fourier-Sine Transforms

G. Steidl, M. Tasche
1991 Mathematics of Computation  
This paper describes 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  ... 
doi:10.2307/2008542 fatcat:tbgodn6y4rfafl7m3ewkdbkgbq

An efficient multiplierless approximation of the fast Fourier transform using sum-of-powers-of-two (SOPOT) coefficients

S.C. Chan, P.M. Yiu
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 .  ... 
doi:10.1109/lsp.2002.803408 fatcat:ovkk4pz5gndufnxwoh2u5lv2ha

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

Jozsef Suto, Stefan Oniga
2015 Elektronika ir Elektrotechnika  
The 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.  ... 
doi:10.5755/j01.eee.21.4.12784 fatcat:zdyogmwnsne4palrr7gyqj2mwe
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