{"id":"https://openalex.org/W7130426809","doi":"https://doi.org/10.1109/msp.2025.3634107","title":"A Pedagogical Reconceptualization of Complex Numbers as Two-Dimensional Real Numbers: A Signal Processing Perspective [Lecture Notes]","display_name":"A Pedagogical Reconceptualization of Complex Numbers as Two-Dimensional Real Numbers: A Signal Processing Perspective [Lecture Notes]","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7130426809","doi":"https://doi.org/10.1109/msp.2025.3634107"},"language":null,"primary_location":{"id":"doi:10.1109/msp.2025.3634107","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2025.3634107","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","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/A5100770168","display_name":"Pushpendra Singh","orcid":null},"institutions":[{"id":"https://openalex.org/I152429107","display_name":"Jawaharlal Nehru University","ror":"https://ror.org/0567v8t28","country_code":"IN","type":"education","lineage":["https://openalex.org/I152429107"]},{"id":"https://openalex.org/I154970844","display_name":"Jaypee Institute of Information Technology","ror":"https://ror.org/05sttyy11","country_code":"IN","type":"education","lineage":["https://openalex.org/I154970844"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Pushpendra Singh","raw_affiliation_strings":["Jaypee Institute of Information Technology, Noida, India","School of Engineering, Jawaharlal Nehru University, New Delhi, India"],"affiliations":[{"raw_affiliation_string":"Jaypee Institute of Information Technology, Noida, India","institution_ids":["https://openalex.org/I154970844"]},{"raw_affiliation_string":"School of Engineering, Jawaharlal Nehru University, New Delhi, India","institution_ids":["https://openalex.org/I152429107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100580762","display_name":"Prisha Singh","orcid":null},"institutions":[{"id":"https://openalex.org/I152429107","display_name":"Jawaharlal Nehru University","ror":"https://ror.org/0567v8t28","country_code":"IN","type":"education","lineage":["https://openalex.org/I152429107"]},{"id":"https://openalex.org/I154970844","display_name":"Jaypee Institute of Information Technology","ror":"https://ror.org/05sttyy11","country_code":"IN","type":"education","lineage":["https://openalex.org/I154970844"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Prisha Singh","raw_affiliation_strings":["Jaypee Institute of Information Technology, Noida, India","School of Engineering, Jawaharlal Nehru University, New Delhi, India"],"affiliations":[{"raw_affiliation_string":"Jaypee Institute of Information Technology, Noida, India","institution_ids":["https://openalex.org/I154970844"]},{"raw_affiliation_string":"School of Engineering, Jawaharlal Nehru University, New Delhi, India","institution_ids":["https://openalex.org/I152429107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123181306","display_name":"Anubha Gupta","orcid":null},"institutions":[{"id":"https://openalex.org/I119939252","display_name":"Indraprastha Institute of Information Technology Delhi","ror":"https://ror.org/03vfp4g33","country_code":"IN","type":"education","lineage":["https://openalex.org/I119939252"]},{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Anubha Gupta","raw_affiliation_strings":["Department of Electronics and Communication Engineering, IIIT-Delhi, New Delhi, India"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Communication Engineering, IIIT-Delhi, New Delhi, India","institution_ids":["https://openalex.org/I119939252","https://openalex.org/I68891433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125475478","display_name":"Rodrigo Capobianco Guido","orcid":null},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Rodrigo Capobianco Guido","raw_affiliation_strings":["São Paulo State University, Brazil"],"affiliations":[{"raw_affiliation_string":"São Paulo State University, Brazil","institution_ids":["https://openalex.org/I879563668"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100770168"],"corresponding_institution_ids":["https://openalex.org/I152429107","https://openalex.org/I154970844"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.89102564,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"1","first_page":"109","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.07760000228881836,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.07760000228881836,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14079","display_name":"Mathematics Education and Programs","score":0.06390000134706497,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14311","display_name":"Electrical and Electromagnetic Research","score":0.0471000000834465,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.7290999889373779},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.6003999710083008},{"id":"https://openalex.org/keywords/multidimensional-signal-processing","display_name":"Multidimensional signal processing","score":0.37929999828338623},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.289900004863739},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.26919999718666077}],"concepts":[{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.7290999889373779},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6844000220298767},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.6003999710083008},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41990000009536743},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.40209999680519104},{"id":"https://openalex.org/C501101116","wikidata":"https://www.wikidata.org/wiki/Q18378116","display_name":"Multidimensional signal processing","level":4,"score":0.37929999828338623},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.2791999876499176},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C94727143","wikidata":"https://www.wikidata.org/wiki/Q485394","display_name":"Analytic signal","level":4,"score":0.26080000400543213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2558000087738037}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/msp.2025.3634107","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2025.3634107","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2064898193","https://openalex.org/W2159136592","https://openalex.org/W3159519317","https://openalex.org/W4293019970","https://openalex.org/W4293498902"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-02-20T06:14:18.993340","created_date":"2026-02-19T00:00:00"}