Empirical evaluation of a sub-linear time sparse DFT algorithm

Empirical evaluation of a sub-linear time sparse DFT algorithm

In this paper we empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time. FADFT-2 returns approximate Fourier representations for frequency-sparse signals and works by random sampling. Its implemen- tation is benchmarked aga...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Communications in mathematical sciences 2007, Vol.5 (4), p.981-998
Hauptverfasser: Gilbert, A., Iwen, M.A., Strauss, M.
Format: Artikel
Sprache:eng
Schlagworte:
65T40
65T50
68W25
68W40
compressive sensing
Fourier transforms
sub-linear time algorithms
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 998
container_issue 4
container_start_page 981
container_title Communications in mathematical sciences
container_volume 5
creator Gilbert, A.
Iwen, M.A.
Strauss, M.
description In this paper we empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time. FADFT-2 returns approximate Fourier representations for frequency-sparse signals and works by random sampling. Its implemen- tation is benchmarked against two competing methods. The first is the popular exact FFT imple- mentation FFTW Version 3.1. The second is an implementation of FADFT-2’s ancestor, FADFT-1. Experiments verify the theoretical runtimes of both FADFT-1 and FADFT-2. In doing so it is shown that FADFT-2 not only generally outperforms FADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals. Furthermore, it is demonstrated that FADFT-2 is indistinguishable from FADFT-1 in terms of noise tolerance despite FADFT-2’s better execution time.
doi_str_mv 10.4310/CMS.2007.v5.n4.a13
format Article
fullrecord <record><control><sourceid>crossref_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_cms_1199377561</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_4310_CMS_2007_v5_n4_a13</sourcerecordid><originalsourceid>FETCH-LOGICAL-c348t-b7ffb8f6ed52e3e23f07cf607e96308f89d1a7e6d8ca545723147c100ad261fb3</originalsourceid><addsrcrecordid>eNo9kF1LwzAYhYMoOKd_wKv8gdak-WpvRKmbChMv3K7D2zTRjH6RtAP_vR0bXp3DgfNcPAjdU5JyRslD-fGVZoSo9CDSjqdA2QVa0IKLhKhCXs5dsCKRistrdBPjnhCqFFcL9LhqBx-8gQbbAzQTjL7vcO8w4DhVSeM7CwGPvrU4DhCixS_rLYbmuw9-_Glv0ZWDJtq7cy7Rbr3alm_J5vP1vXzeJIbxfEwq5VyVO2lrkVlmM-aIMk4SZQvJSO7yoqagrKxzA4ILlTHKlaGEQJ1J6iq2RE8n7hD6vTWjnUzjaz0E30L41T14Xe425_Ucpo2a0qJgSglJZ0R2QpjQxxis-39Too8S9SxRHyXqg9Ad17NE9gd2amcg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Empirical evaluation of a sub-linear time sparse DFT algorithm</title><source>International Press Journals</source><source>EZB Free E-Journals</source><creator>Gilbert, A. ; Iwen, M.A. ; Strauss, M.</creator><creatorcontrib>Gilbert, A. ; Iwen, M.A. ; Strauss, M.</creatorcontrib><description>In this paper we empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time. FADFT-2 returns approximate Fourier representations for frequency-sparse signals and works by random sampling. Its implemen- tation is benchmarked against two competing methods. The first is the popular exact FFT imple- mentation FFTW Version 3.1. The second is an implementation of FADFT-2’s ancestor, FADFT-1. Experiments verify the theoretical runtimes of both FADFT-1 and FADFT-2. In doing so it is shown that FADFT-2 not only generally outperforms FADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals. Furthermore, it is demonstrated that FADFT-2 is indistinguishable from FADFT-1 in terms of noise tolerance despite FADFT-2’s better execution time.</description><identifier>ISSN: 1539-6746</identifier><identifier>EISSN: 1945-0796</identifier><identifier>DOI: 10.4310/CMS.2007.v5.n4.a13</identifier><language>eng</language><publisher>International Press of Boston</publisher><subject>65T40 ; 65T50 ; 68W25 ; 68W40 ; compressive sensing ; Fourier transforms ; sub-linear time algorithms</subject><ispartof>Communications in mathematical sciences, 2007, Vol.5 (4), p.981-998</ispartof><rights>Copyright 2007 International Press of Boston</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c348t-b7ffb8f6ed52e3e23f07cf607e96308f89d1a7e6d8ca545723147c100ad261fb3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,4024,27923,27924,27925</link.rule.ids></links><search><creatorcontrib>Gilbert, A.</creatorcontrib><creatorcontrib>Iwen, M.A.</creatorcontrib><creatorcontrib>Strauss, M.</creatorcontrib><title>Empirical evaluation of a sub-linear time sparse DFT algorithm</title><title>Communications in mathematical sciences</title><description>In this paper we empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time. FADFT-2 returns approximate Fourier representations for frequency-sparse signals and works by random sampling. Its implemen- tation is benchmarked against two competing methods. The first is the popular exact FFT imple- mentation FFTW Version 3.1. The second is an implementation of FADFT-2’s ancestor, FADFT-1. Experiments verify the theoretical runtimes of both FADFT-1 and FADFT-2. In doing so it is shown that FADFT-2 not only generally outperforms FADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals. Furthermore, it is demonstrated that FADFT-2 is indistinguishable from FADFT-1 in terms of noise tolerance despite FADFT-2’s better execution time.</description><subject>65T40</subject><subject>65T50</subject><subject>68W25</subject><subject>68W40</subject><subject>compressive sensing</subject><subject>Fourier transforms</subject><subject>sub-linear time algorithms</subject><issn>1539-6746</issn><issn>1945-0796</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNo9kF1LwzAYhYMoOKd_wKv8gdak-WpvRKmbChMv3K7D2zTRjH6RtAP_vR0bXp3DgfNcPAjdU5JyRslD-fGVZoSo9CDSjqdA2QVa0IKLhKhCXs5dsCKRistrdBPjnhCqFFcL9LhqBx-8gQbbAzQTjL7vcO8w4DhVSeM7CwGPvrU4DhCixS_rLYbmuw9-_Glv0ZWDJtq7cy7Rbr3alm_J5vP1vXzeJIbxfEwq5VyVO2lrkVlmM-aIMk4SZQvJSO7yoqagrKxzA4ILlTHKlaGEQJ1J6iq2RE8n7hD6vTWjnUzjaz0E30L41T14Xe425_Ucpo2a0qJgSglJZ0R2QpjQxxis-39Too8S9SxRHyXqg9Ad17NE9gd2amcg</recordid><startdate>2007</startdate><enddate>2007</enddate><creator>Gilbert, A.</creator><creator>Iwen, M.A.</creator><creator>Strauss, M.</creator><general>International Press of Boston</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2007</creationdate><title>Empirical evaluation of a sub-linear time sparse DFT algorithm</title><author>Gilbert, A. ; Iwen, M.A. ; Strauss, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c348t-b7ffb8f6ed52e3e23f07cf607e96308f89d1a7e6d8ca545723147c100ad261fb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>65T40</topic><topic>65T50</topic><topic>68W25</topic><topic>68W40</topic><topic>compressive sensing</topic><topic>Fourier transforms</topic><topic>sub-linear time algorithms</topic><toplevel>online_resources</toplevel><creatorcontrib>Gilbert, A.</creatorcontrib><creatorcontrib>Iwen, M.A.</creatorcontrib><creatorcontrib>Strauss, M.</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gilbert, A.</au><au>Iwen, M.A.</au><au>Strauss, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Empirical evaluation of a sub-linear time sparse DFT algorithm</atitle><jtitle>Communications in mathematical sciences</jtitle><date>2007</date><risdate>2007</risdate><volume>5</volume><issue>4</issue><spage>981</spage><epage>998</epage><pages>981-998</pages><issn>1539-6746</issn><eissn>1945-0796</eissn><abstract>In this paper we empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time. FADFT-2 returns approximate Fourier representations for frequency-sparse signals and works by random sampling. Its implemen- tation is benchmarked against two competing methods. The first is the popular exact FFT imple- mentation FFTW Version 3.1. The second is an implementation of FADFT-2’s ancestor, FADFT-1. Experiments verify the theoretical runtimes of both FADFT-1 and FADFT-2. In doing so it is shown that FADFT-2 not only generally outperforms FADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals. Furthermore, it is demonstrated that FADFT-2 is indistinguishable from FADFT-1 in terms of noise tolerance despite FADFT-2’s better execution time.</abstract><pub>International Press of Boston</pub><doi>10.4310/CMS.2007.v5.n4.a13</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1539-6746
ispartof Communications in mathematical sciences, 2007, Vol.5 (4), p.981-998
issn 1539-6746
1945-0796
language eng
recordid cdi_projecteuclid_primary_oai_CULeuclid_euclid_cms_1199377561
source International Press Journals; EZB Free E-Journals
subjects 65T40
65T50
68W25
68W40
compressive sensing
Fourier transforms
sub-linear time algorithms
title Empirical evaluation of a sub-linear time sparse DFT algorithm
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-03T14%3A27%3A18IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Empirical%20evaluation%20of%20a%20sub-linear%20time%20sparse%20DFT%20algorithm&rft.jtitle=Communications%20in%20mathematical%20sciences&rft.au=Gilbert,%20A.&rft.date=2007&rft.volume=5&rft.issue=4&rft.spage=981&rft.epage=998&rft.pages=981-998&rft.issn=1539-6746&rft.eissn=1945-0796&rft_id=info:doi/10.4310/CMS.2007.v5.n4.a13&rft_dat=%3Ccrossref_proje%3E10_4310_CMS_2007_v5_n4_a13%3C/crossref_proje%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true