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An algorithm for fast computation of the multiresolution discrete Fourier transform [article]

Bartosz Andreatto, Aleksandr Cariow
<span title="2015-07-09">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT).  ...  This allows for the use of a computational process parallelization and results in a reduction of computation time.  ...  DEVELOPMENT OF THE RATIONALIZED ALGORITHM FOR CALCULATING THE MULTIRESOLUTION DISCRETE FOURIER TRANSFORM The approach presented in this article consists in the realization of the fast Fourier transform  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.02525v1">arXiv:1507.02525v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/afv4dbmtirg2phcbywswydogse">fatcat:afv4dbmtirg2phcbywswydogse</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200929175857/https://arxiv.org/ftp/arxiv/papers/1507/1507.02525.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ab/96/ab962aa18d42a8b5fdadd0507a72ea8562d46ba6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.02525v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Novel algorithms for 2-D FFT and its inverse for image compression

T. G. Anitha, S. Ramachandran
<span title="">2013</span> <i title="IEEE"> 2013 International Conference on Signal Processing , Image Processing &amp; Pattern Recognition </i> &nbsp;
High performance Fast Fourier Transform and Inverse Fast Fourier Transform are indispensable algorithms in the field of Digital Signal Processing.  ...  The algorithms have been developed to suit VLSI realization, where the processing speed is of paramount importance.  ...  The Fast Fourier Transform is an efficient algorithm to compute the Discrete Fourier Transform (DFT) fast and its inverse. The evaluation of both produces same results but FFT is much faster.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icsipr.2013.6497959">doi:10.1109/icsipr.2013.6497959</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qene5362endbrcgus7yi2n3jmq">fatcat:qene5362endbrcgus7yi2n3jmq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809033319/https://www.mathworks.com/matlabcentral/answers/uploaded_files/31709/IEEE%202013%20Image%20Comp..pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9f/78/9f78bf75e3a1fc2b8c80f4c18b1bdcc2639f24c8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/icsipr.2013.6497959"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Page 6220 of Mathematical Reviews Vol. , Issue 96j [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Our approach is based on the asymptotic expansion of the symbol together with the fast Fourier transform (FFT).  ...  The Fourier transform of f (with respect to #) is defined as the set of matrices {f (p)}pca- Recovery of f from its Fourier transform may be accomplished via the Fourier inversion formula, f(s)= a po d  ... 
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A fast algorithm for solving the first biharmonic boundary value problem

M. Vajteršic
<span title="">1979</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dusph3ot3rfilc55znthn7tkmu" style="color: black;">Computing</a> </i> &nbsp;
The parallel implementation would call for an architecture which would allow to perform the fast Fourier transform and the inner product of real vectors in an efficient way.  ...  The evaluation of one iteration will include some steps with 0(n 2 ) complexity and 2n real Fourier transforms of vectors of the length n.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf02252095">doi:10.1007/bf02252095</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7vrs2i6hqzb53indf5pzlotknu">fatcat:7vrs2i6hqzb53indf5pzlotknu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170813165004/http://dml.cz/bitstream/handle/10338.dmlcz/104140/AplMat_30-1985-3_4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/50/64/5064ff2681626ee68543e331e0ca7d64f0369a5e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf02252095"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A frequency-weighted block LMS algorithm and its application to speech processing

J.C. Lee, C.K. Un, D.H. Cho
<span title="">1985</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yfvtieuumfamvmjlc255uckdlm" style="color: black;">Proceedings of the IEEE</a> </i> &nbsp;
They are defined as and where F is the ( N X N ) discrete Fourier transform matrix, I , and I,( denote ( L X L ) and (h1 X hi) Identity matrices, respectively, and 0 is a zero matrix.  ...  In ( I ) . the t w o ( N X N ) matrices Yo [ and Bhf,o realize the sectioning procedures needed for computing the filter output and adjusting the filter weights, respectively.  ...  The authors are with the Department of Physics, The Catholic Univer-0018-9219/85/0600~1138%01.00 a 9 8 5 IEEE  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/proc.1985.13245">doi:10.1109/proc.1985.13245</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iciwwex4xjfvdeedpewww3gdu4">fatcat:iciwwex4xjfvdeedpewww3gdu4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829061403/http://koasas.kaist.ac.kr/bitstream/10203/130/1/02_a%20frequency%20weighted%20block%20LMS%20algorithm%20and%20its%20application%20to%20speech%20processing.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bb/73/bb73dd5719507cc4dcff5451bea65353231556f7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/proc.1985.13245"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Page 4807 of Mathematical Reviews Vol. , Issue 81K [page]

<span title="">1981</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
realization of the fast Fourier transformation of NXN matrices.  ...  Thus the realization of the FFT of N <x N matrices can be obtained in log, N —1 computational steps, each of them with N? parallel performable multiplications. B. D. Donevski (Sofia) Aly, Samy A.  ... 
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Approximate Fast Graph Fourier Transforms via Multilayer Sparse Approximations

Luc Le Magoarou, Remi Gribonval, Nicolas Tremblay
<span title="">2018</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rvtgectofngnzecuror33aohae" style="color: black;">IEEE Transactions on Signal and Information Processing over Networks</a> </i> &nbsp;
The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations.  ...  It is based on a greedy approximate diagonalization of the graph Laplacian matrix, carried out using a modified version of the famous Jacobi eigenvalues algorithm.  ...  ACKNOWLEDGMENT The authors would like to thank Igal Rozenberg for discussions and collaboration on the topic of graph signal processing during his internship with the team.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsipn.2017.2710619">doi:10.1109/tsipn.2017.2710619</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/itwkhdy2tvd25fcymkjvwhk7su">fatcat:itwkhdy2tvd25fcymkjvwhk7su</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180724080349/https://hal.inria.fr/hal-01416110/document" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d3/3e/d33ed0d85214fd98f3f439fa15fe83f93cdbe8a9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsipn.2017.2710619"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Indigo: A Domain-Specific Language for Fast, Portable Image Reconstruction

Michael Driscoll, Benjamin Brock, Frank Ong, Jonathan Tamir, Hsiou-Yuan Liu, Michael Lustig, Armando Fox, Katherine Yelick
<span title="">2018</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t3x4vqewrncrfgn2wu7cafsbsq" style="color: black;">2018 IEEE International Parallel and Distributed Processing Symposium (IPDPS)</a> </i> &nbsp;
, etc.) of the leaf operators.  ...  The matrix-driven approach is generally more portable because it can target widelyavailable BLAS libraries, but it can be inefficient in terms of time and space complexity.  ...  ACKNOWLEDGMENTS This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ipdps.2018.00059">doi:10.1109/ipdps.2018.00059</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ipps/DriscollBOTLLFY18.html">dblp:conf/ipps/DriscollBOTLLFY18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o5alcooghbcrfmnlxntj5u5yf4">fatcat:o5alcooghbcrfmnlxntj5u5yf4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201107133949/https://escholarship.org/content/qt1hk8966m/qt1hk8966m.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bd/f9/bdf93fe0f581480440dcb3e2cfa172f977acbb7a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ipdps.2018.00059"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Invariant spaces and cosine transforms DCT - 2 and DCT - 6

Bozhan Zhechev
<span title="">2004</span> <i title="ACM Press"> Proceedings of the 5th international conference on Computer systems and technologies - CompSysTech &#39;04 </i> &nbsp;
The discrete cosine (and sine) transforms (DCT/DST) are analyzed in this paper on the basis of the linear representations of finite groups and geometrical approach.  ...  It is shown that if the Discrete Fourier Transform (DFT) operator is referred to an appropriate basis it takes a block-diagonal form.  ...  Results received in this paper solve the task for the fast realizations of these transforms; all they are derivatives of the DFT, and sparse matrices implement the connections.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1050330.1050349">doi:10.1145/1050330.1050349</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eij5xcpjava4dktece6xhxg7a4">fatcat:eij5xcpjava4dktece6xhxg7a4</a> </span>
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Quantum computing and a unified approach to fast unitary transforms

Sos S. Agaian, Andreas Klappenecker, Edward R. Dougherty, Jaakko T. Astola, Karen O. Egiazarian
<span title="2002-05-23">2002</span> <i title="SPIE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/n3ge7z6hafchpio7czlg3oqamm" style="color: black;">Image Processing: Algorithms and Systems</a> </i> &nbsp;
We show how fast quantum algorithms can be derived for the discrete Fourier transform, the Walsh-Hadamard transform, the Slant transform, and the Hartley transform.  ...  All these algorithms use at most O(log^2 N) operations to transform a state vector of a quantum computer of length N.  ...  For instance, the discrete Fourier transform of length N = 2 n can be implemented with O(log 2 N ) operations on a quantum computer.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1117/12.467967">doi:10.1117/12.467967</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ipas/AgaianK02.html">dblp:conf/ipas/AgaianK02</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g5xszv35tbdhtewjantnqpfjyy">fatcat:g5xszv35tbdhtewjantnqpfjyy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180727202800/http://cds.cern.ch/record/535909/files/0201120.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/87/09/8709ea55d57d97c165aec7948f0b4813b443235f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1117/12.467967"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Matrix-Vector Based Fast Fourier Transformations on SDR Architectures

Y. He, K. Hueske, J. Götze, E. Coersmeier
<span title="2008-05-26">2008</span> <i title="Copernicus GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tghxjwqxwbai7kts5acw24xizm" style="color: black;">Advances in Radio Science</a> </i> &nbsp;
It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT) engines.  ...  </strong> Today Discrete Fourier Transforms (DFTs) are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex).  ...  Discrete Fourier Transform (DFT) The sequence of N (with N=2 m , m∈ N) complex numbers x 1 , · · ·, x N is transformed into the sequence of N complex numbers y 1 , · · ·, y N by the DFT according to y  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5194/ars-6-89-2008">doi:10.5194/ars-6-89-2008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dqc6m5n72vbhfl7vao6ixzn5oa">fatcat:dqc6m5n72vbhfl7vao6ixzn5oa</a> </span>
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Page 427 of Mathematical Reviews Vol. , Issue 92a [page]

<span title="">1992</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “There are two ways, other than the standard fast Fou- rier transform (FFT) algorithm, of computing Fourier transforms of real data, namely, (1) the real fast Fourier transform (RFFT) al- gorithm  ...  E. (1-ODM) Computing the Fourier transform of real data on a hypercube. J. Sci. Comput. 5 (1990), no. 4, 293-309.  ... 
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Fast Analysis of On-Chip Power Grid Circuits by Extended Truncated Balanced Realization Method

Duo LI, Sheldon X.-D. TAN
<span title="">2009</span> <i title="Institute of Electronics, Information and Communications Engineers (IEICE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x2mklbxoqjfvjdjrdybgo53sdm" style="color: black;">IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences</a> </i> &nbsp;
ETBR also avoids the adverse explicit moment representation of the input signals. Instead, it uses spectrum representation in frequency domain for input signals by fast Fourier transformation.  ...  The new approach, called ETBR for extended truncated balanced realization, is based on model order reduction techniques to reduce the circuit matrices before the simulation.  ...  Instead, it uses spectrum representation of input signals by fast Fourier transformation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1587/transfun.e92.a.3061">doi:10.1587/transfun.e92.a.3061</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lap6utpgpfdqldiqtdg5k5gnwa">fatcat:lap6utpgpfdqldiqtdg5k5gnwa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20161201020126/http://www.ee.ucr.edu/~stan/papers/ieice09etbr.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/57/45/5745cc1720bfd0dcecef4b88a0fcb926bb3827c3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1587/transfun.e92.a.3061"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

A Parallel Preconditioned Iterative Realization of the Panel Method in 3D

Matthias Pester, Sergej Rjasanow
<span title="">1996</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qctbh4zvsja6bkoj73ijn57zhy" style="color: black;">Numerical Linear Algebra with Applications</a> </i> &nbsp;
KEY WORDS boundary value problem, boundary element method, preconditioning, iterative method, Fast Fourier Transform, parallel algorithm  ...  The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary  ...  m 2 n lnn arithmetic operations for the entire alorithm if we use the Fast Fourier Transform (see 2]) twice at steps 1 and 3.2.The preparation step is the numerical solution of n complete eigenvalue problems  ... 
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A Parallel Preconditioned Iterative Realization of the Panel Method in 3D

Matthias Pester, Sergej Rjasanow
<span title="">1996</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qctbh4zvsja6bkoj73ijn57zhy" style="color: black;">Numerical Linear Algebra with Applications</a> </i> &nbsp;
KEY WORDS boundary value problem, boundary element method, preconditioning, iterative method, Fast Fourier Transform, parallel algorithm  ...  The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary  ...  m 2 n lnn arithmetic operations for the entire alorithm if we use the Fast Fourier Transform (see 2]) twice at steps 1 and 3.2.The preparation step is the numerical solution of n complete eigenvalue problems  ... 
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