{"id":"https://openalex.org/W2159941611","doi":"https://doi.org/10.1109/tc.1973.5009139","title":"Comments on \"On the Definition and Generation of Walsh Functions","display_name":"Comments on \"On the Definition and Generation of Walsh Functions","publication_year":1973,"publication_date":"1973-07-01","ids":{"openalex":"https://openalex.org/W2159941611","doi":"https://doi.org/10.1109/tc.1973.5009139","mag":"2159941611"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1973.5009139","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1973.5009139","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Computers","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/A5091672762","display_name":"Jochen Till","orcid":null},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"J. W. J. Van Till","raw_affiliation_strings":["Department odf Electrical Engineering, Delft University of Technnology, Delft, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department odf Electrical Engineering, Delft University of Technnology, Delft, Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091672762"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.29245742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"C-22","issue":"7","first_page":"702","last_page":"703"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.8421000242233276,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.8421000242233276,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.7627000212669373,"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/walsh-function","display_name":"Walsh function","score":0.8343561291694641},{"id":"https://openalex.org/keywords/decimal","display_name":"Decimal","score":0.6070441007614136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5879430770874023},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5705318450927734},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5078828930854797},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41857367753982544},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4083136320114136},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4068002998828888},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35030025243759155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3457511067390442},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1854018270969391},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15234586596488953}],"concepts":[{"id":"https://openalex.org/C164319782","wikidata":"https://www.wikidata.org/wiki/Q1934233","display_name":"Walsh function","level":2,"score":0.8343561291694641},{"id":"https://openalex.org/C65045869","wikidata":"https://www.wikidata.org/wiki/Q81365","display_name":"Decimal","level":2,"score":0.6070441007614136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5879430770874023},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5705318450927734},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5078828930854797},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41857367753982544},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4083136320114136},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4068002998828888},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35030025243759155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3457511067390442},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1854018270969391},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15234586596488953},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1973.5009139","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1973.5009139","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1982022511","https://openalex.org/W1985133056"],"related_works":["https://openalex.org/W2350482071","https://openalex.org/W2516369861","https://openalex.org/W177032641","https://openalex.org/W2502533382","https://openalex.org/W1967012415","https://openalex.org/W2961151343","https://openalex.org/W2468097068","https://openalex.org/W3028928340","https://openalex.org/W279796016","https://openalex.org/W2078540024"],"abstract_inverted_index":{"A":[0],"correction":[1],"to":[2],"the":[3,20,44],"Gray":[4],"code-to-decimal":[5],"conversion":[6],"of":[7,22,36,46],"Davies":[8],"is":[9,39],"given,":[10,41],"which":[11],"follows":[12],"from":[13,43],"Davies'":[14],"own":[15],"proof":[16,30],"if":[17],"performed":[18],"on":[19,24],"level":[21],"operations":[23],"wave":[25],"number":[26],"indices.":[27],"An":[28],"alternative":[29],"for":[31],"Walsh":[32],"functions":[33,38],"as":[34],"combinations":[35],"Rademacher":[37],"also":[40],"starting":[42],"definition":[45],"Walsh-Kaczmarz":[47],"functions.":[48]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
