{"id":"https://openalex.org/W2020012860","doi":"https://doi.org/10.1137/130932533","title":"Discrete Periodic Extension Using an Approximate Step Function","display_name":"Discrete Periodic Extension Using an Approximate Step Function","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2020012860","doi":"https://doi.org/10.1137/130932533","mag":"2020012860"},"language":"en","primary_location":{"id":"doi:10.1137/130932533","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932533","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5036022357","display_name":"Nathan Albin","orcid":"https://orcid.org/0000-0002-3973-1471"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nathan Albin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049113167","display_name":"Sureka Pathmanathan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sureka Pathmanathan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036022357"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2439,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.57524416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"36","issue":"2","first_page":"A668","last_page":"A692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9994999766349792,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9994999766349792,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.8426270484924316},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7984523773193359},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.5755050778388977},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5318135023117065},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.5145716071128845},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5139736533164978},{"id":"https://openalex.org/keywords/trigonometric-polynomial","display_name":"Trigonometric polynomial","score":0.5100020170211792},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4927826225757599},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.4922739565372467},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4761604964733124},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.45425912737846375},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4426543712615967},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.42183905839920044},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4164283275604248},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3875594735145569},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.36492031812667847},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26001641154289246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14738133549690247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12352359294891357},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08335793018341064}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.8426270484924316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7984523773193359},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.5755050778388977},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5318135023117065},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.5145716071128845},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5139736533164978},{"id":"https://openalex.org/C156760230","wikidata":"https://www.wikidata.org/wiki/Q1969650","display_name":"Trigonometric polynomial","level":3,"score":0.5100020170211792},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4927826225757599},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.4922739565372467},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4761604964733124},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.45425912737846375},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4426543712615967},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.42183905839920044},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4164283275604248},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3875594735145569},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.36492031812667847},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26001641154289246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14738133549690247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12352359294891357},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08335793018341064},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130932533","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932533","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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":23,"referenced_works":["https://openalex.org/W203940937","https://openalex.org/W584547061","https://openalex.org/W1805381866","https://openalex.org/W1843683759","https://openalex.org/W1996481970","https://openalex.org/W2020044270","https://openalex.org/W2036740708","https://openalex.org/W2041410208","https://openalex.org/W2043134554","https://openalex.org/W2045974403","https://openalex.org/W2052788839","https://openalex.org/W2055315600","https://openalex.org/W2066187209","https://openalex.org/W2066313543","https://openalex.org/W2074722757","https://openalex.org/W2080219236","https://openalex.org/W2088818994","https://openalex.org/W2113499611","https://openalex.org/W2117804954","https://openalex.org/W2124998631","https://openalex.org/W2125953366","https://openalex.org/W2138286512","https://openalex.org/W2165446729"],"related_works":["https://openalex.org/W634571496","https://openalex.org/W579400037","https://openalex.org/W2951578208","https://openalex.org/W1570037808","https://openalex.org/W4298173607","https://openalex.org/W4387031439","https://openalex.org/W4386784405","https://openalex.org/W630157503","https://openalex.org/W2153015377","https://openalex.org/W2805114793"],"abstract_inverted_index":{"The":[0,53,72],"discrete":[1,54,95],"periodic":[2,55,96],"extension":[3,25,30,56,97],"is":[4,31,57],"a":[5,9,17,28,58,92],"technique":[6],"for":[7],"augmenting":[8],"given":[10],"set":[11],"of":[12,16,51,81],"uniformly":[13],"spaced":[14],"samples":[15],"smooth":[18],"function":[19,46],"with":[20,110],"auxiliary":[21],"values":[22],"in":[23,47,61,75],"an":[24,39],"region.":[26],"If":[27],"suitable":[29],"constructed,":[32],"the":[33,44,62,79,106],"interpolating":[34],"trigonometric":[35],"polynomial":[36],"found":[37],"via":[38],"FFT":[40],"will":[41],"accurately":[42],"approximate":[43],"original":[45,49],"its":[48],"interval":[50],"definition.":[52],"key":[59],"construction":[60],"algorithm":[63],"FC-Gram":[64,73,107],"(Fourier":[65],"continuation":[66],"based":[67],"on":[68],"Gram":[69],"polynomials)":[70],"algorithm.":[71],"algorithm,":[74],"turn,":[76],"lies":[77],"at":[78,101],"heart":[80],"several":[82],"recent":[83],"efficient":[84],"and":[85,114],"high-order-accurate":[86],"PDE":[87],"solvers.":[88],"This":[89],"paper":[90],"presents":[91],"new":[93],"flexible":[94],"procedure":[98],"that":[99],"performs":[100],"least":[102],"as":[103,105],"well":[104],"method,":[108],"but":[109],"somewhat":[111],"simpler":[112],"constructions":[113],"significantly":[115],"decreased":[116],"setup":[117],"time.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}