{"id":"https://openalex.org/W2074398797","doi":"https://doi.org/10.1109/tassp.1985.1164736","title":"Construction of group transforms subject to several performance criteria","display_name":"Construction of group transforms subject to several performance criteria","publication_year":1985,"publication_date":"1985-12-01","ids":{"openalex":"https://openalex.org/W2074398797","doi":"https://doi.org/10.1109/tassp.1985.1164736","mag":"2074398797"},"language":"en","primary_location":{"id":"doi:10.1109/tassp.1985.1164736","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1985.1164736","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Acoustics, Speech, and Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034459123","display_name":"Estherina Trachtenberg","orcid":"https://orcid.org/0009-0005-1763-5218"},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"E. Trachtenberg","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA","Drexal University, Philadelphia, PA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I72816309"]},{"raw_affiliation_string":"Drexal University, Philadelphia, PA","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034459123"],"corresponding_institution_ids":["https://openalex.org/I72816309"],"apc_list":null,"apc_paid":null,"fwci":1.1456,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77700348,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"6","first_page":"1521","last_page":"1531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9672999978065491,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6709828972816467},{"id":"https://openalex.org/keywords/hilbert-transform","display_name":"Hilbert transform","score":0.6361067891120911},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.5656877160072327},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.5651206374168396},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5276773571968079},{"id":"https://openalex.org/keywords/s-transform","display_name":"S transform","score":0.4704538583755493},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4588298499584198},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4544738233089447},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4476357400417328},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.43934255838394165},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4309290051460266},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.4283777177333832},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.41967490315437317},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3653804063796997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19449570775032043},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07886284589767456},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07864141464233398},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07463023066520691},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.07269984483718872}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6709828972816467},{"id":"https://openalex.org/C28799612","wikidata":"https://www.wikidata.org/wiki/Q685437","display_name":"Hilbert transform","level":3,"score":0.6361067891120911},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.5656877160072327},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.5651206374168396},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5276773571968079},{"id":"https://openalex.org/C99234102","wikidata":"https://www.wikidata.org/wiki/Q7395403","display_name":"S transform","level":5,"score":0.4704538583755493},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4588298499584198},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4544738233089447},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4476357400417328},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.43934255838394165},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4309290051460266},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.4283777177333832},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.41967490315437317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3653804063796997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19449570775032043},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07886284589767456},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07864141464233398},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07463023066520691},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.07269984483718872},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.0},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tassp.1985.1164736","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1985.1164736","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Acoustics, Speech, and Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1505677421","https://openalex.org/W1975877782","https://openalex.org/W1990535777","https://openalex.org/W1992283714","https://openalex.org/W2000108174","https://openalex.org/W2004450764","https://openalex.org/W2018001450","https://openalex.org/W2022984904","https://openalex.org/W2028788342","https://openalex.org/W2045996359","https://openalex.org/W2046344940","https://openalex.org/W2059734651","https://openalex.org/W2083035009","https://openalex.org/W2141262522","https://openalex.org/W2141612050","https://openalex.org/W2144640755","https://openalex.org/W2145341540","https://openalex.org/W2154311960","https://openalex.org/W2283540854","https://openalex.org/W2312235895","https://openalex.org/W2520489697","https://openalex.org/W3021757444","https://openalex.org/W4211258748","https://openalex.org/W4239894305","https://openalex.org/W4244401852","https://openalex.org/W6630365737","https://openalex.org/W6726771496"],"related_works":["https://openalex.org/W1992851990","https://openalex.org/W2038618959","https://openalex.org/W2115327346","https://openalex.org/W2358130123","https://openalex.org/W2606546932","https://openalex.org/W1605622899","https://openalex.org/W1482372743","https://openalex.org/W2385275966","https://openalex.org/W2393765384","https://openalex.org/W3019335580"],"abstract_inverted_index":{"A":[0],"transform,":[1],"L,":[2],"is":[3,95,111,130,140],"defined":[4],"in":[5,29,54,125],"this":[6],"paper":[7],"and":[8,19,214],"studied":[9],"subject":[10],"to":[11,32,72,84,97,150,157,176,207],"the":[12,33,40,73,86,92,126,145,152,160,192,202,211],"two":[13,74,138],"opposing":[14],"performance":[15,88],"criteria,":[16],"computational":[17,87,107,153],"effectiveness":[18],"accuracy":[20],"of":[21,23,46,78,89,109,121,136,155,159,170,200],"approximation":[22],"a":[24,43,102,119,182],"given":[25,103,183],"unitary":[26,104,184],"transform":[27,163],"measured":[28],"distance":[30,100,179],"related":[31],"Hilbert-Sehmidt":[34],"norm.":[35],"The":[36,106],"matrices":[37,123],"which":[38,49],"represent":[39],"L-transform":[41],"constitute":[42],"special":[44],"class":[45],"group":[47],"matrices,":[48],"were":[50],"introduced":[51],"by":[52,113],"Frobenius":[53],"1895.":[55],"These":[56],"(n":[57],"\u00d7":[58],"n)-matrices":[59],"depend":[60],"upon":[61],"certain":[62],"free":[63],"parameters":[64,80,146,172,194,204],"whose":[65],"choice":[66],"determines":[67],"their":[68],"behavior":[69],"with":[70,209],"respect":[71],"criteria.":[75],"Hence,":[76],"part":[77,94],"these":[79,137,171],"can":[81,147,173],"be":[82,148,174],"chosen":[83],"affect":[85],"L":[90,110,115,156],"whereas":[91],"other":[93,212],"used":[96,141,149,175,197],"minimize":[98],"its":[99],"from":[101,181],"transform.":[105,185],"complexity":[108,154],"eased":[112],"making":[114],"sparse":[116,122],"rather":[117],"than":[118],"product":[120],"as":[124],"FFT":[127],"algorithm.":[128],"It":[129],"shown":[131],"that":[132,158,195],"if":[133],"only":[134],"one":[135,199,213],"criteria":[139,188],"then":[142,191],"either":[143],"all":[144,169],"reduce":[151],"fast":[161],"Haar":[162],"(in":[164],"nontrivial":[165],"cases)":[166],"or":[167],"else":[168],"achieve":[177],"(asymptotically)":[178],"zero":[180],"If":[186],"both":[187],"are":[189,196,222],"used,":[190],"more":[193],"for":[198,210],"them,":[201],"less":[203],"we":[205],"have":[206],"deal":[208],"vice":[215],"versa-an":[216],"inverse":[217],"proportional":[218],"dependence.":[219],"Various":[220],"examples":[221],"given.":[223]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
