Complex-Valued Signals: a Tutorial for Non-Circular Data Processing and Analysis

Authors

  • Rafael Bluhm UFC https://orcid.org/0009-0003-4942-1535
  • João César Moura Mota Universidade Federal do Ceará
  • Charles Casimiro Cavalcante Universidade Federal do Ceará

DOI:

https://doi.org/10.14209/jcis.2025.07

Keywords:

Complex-valued, Widely linear, Improper signals

Abstract

This work explores the versatility of complex-valued signals present in data representation in diverse applications. Integrating complex values into signals and processing structures proves powerful in system modeling, demonstrating effectiveness in many scenarios. The inherent mathematical efficiency of complex numbers enhances both elegance and practical utility, simplifying calculations and expanding capabilities. However, the use of complex notation introduces considerations related to the intrinsic geometry of the data. This tutorial unravels the theoretical foundations and practical applications in adaptive filtering of complex-valued signals, emphasizing the importance of understanding the displayed profiles of the studied signals and data. Using complex augmented notation and widely linear processing, superior performance is attainable in specific cases, providing valuable information to readers interested in signal processing.

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Author Biographies

João César Moura Mota, Universidade Federal do Ceará

João C. M. Mota received the BS degree in physics from the Federal University of Ceará, Fortaleza, Brazil, in 1978, the MSc degree in electrical engineering from the Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil, in 1984, and the PhD degree in electrical engineering from the State University of Campinas, Campinas, Brazil, in 1992. He is currently a professor at the Federal University of Ceará and the assistant director for Interinstitutional Relationships of its Technology Center, founding member of the Brazilian Society of Telecommunications, member of the Brazilian Society of Health Informatics, adviser to the Student Branch of the Institute of Electrical and Electronics Engineers (IEEE) in FUC, and member of the Signal Processing Society and IEEE Communications Society.

Charles Casimiro Cavalcante, Universidade Federal do Ceará

Charles C. Cavalcante (Senior Member, IEEE) received the B.Sc. and M.Sc. degrees in electrical engineering from the Federal University of Ceará (UFC), Brazil, in 1999 and 2001, respectively, and the Ph.D. degree from the University of Campinas (UNICAMP), Brazil, in 2004. He received grants for Scientific and Technological Development from 2004 to 2007 and Scientific Research Productivity from the Brazilian Research Council (CNPq) since March 2009. He is currently an Associate Professor with the Teleinformatics Engineering Department, UFC, holding the Statistical Signal Processing Chair. From August 2014 to July 2015, he was a Visiting Assistant Professor with the Department of Computer Science and Electrical Engineering (CSEE), University of Maryland Baltimore County (UMBC), USA. He has been working on signal processing strategies for communications, where he has published several papers in journals and conferences, has authored three international patents, and has worked on several funded research projects on the signal processing and wireless communications areas. He is also the coauthor of the book Unsupervised Signal Processing: Channel Equalization and Source Separation (CRC Press) and a co-editor of the book Signals and Images: Advances and Results in Speech, Estimation, Compression, Recognition, Filtering, and Processing (CRC Press). He is a Senior Member of the Brazilian Telecommunications Society (SBrT). He was the President of the Brazilian Telecommunication Society (SBrT) for the term (2018–2020) and the IEEE Signal Processing Society Regional Director-at-Large for Regions 7 & 9 for the term (2020–2021). His main research interests include signal processing for communications, statistical signal processing, machine learning, and information geometry.

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Published

2025-10-07

How to Cite

Bluhm, R., Mota, J. C. M., & Cavalcante, C. C. (2025). Complex-Valued Signals: a Tutorial for Non-Circular Data Processing and Analysis. Journal of Communication and Information Systems, 40(1), 47–73. https://doi.org/10.14209/jcis.2025.07

Issue

Vol. 40 No. 1 (2025)

Section

Tutorial Papers

License

Copyright (c) 2025 Rafael Bluhm, João César Moura Mota, Charles Casimiro Cavalcante (Author)

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Received 2025-05-29
Accepted 2025-09-09
Published 2025-10-07