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A Vector Representation of Multicomplex Numbers and Its Application to Radio Frequency Signals.
- Source :
-
Axioms (2075-1680) . May2024, Vol. 13 Issue 5, p324. 20p. - Publication Year :
- 2024
-
Abstract
- Hypercomplex numbers, which are multi-dimensional extensions of complex numbers, have been proven beneficial in the development of advanced signal processing algorithms, including multi-dimensional filter design, linear regression and classification. We focus on multicomplex numbers, sets of hypercomplex numbers with commutative products, and introduce a vector representation allowing one to isolate the hyperbolic real and imaginary parts of a multicomplex number. The orthogonal decomposition of a multicomplex number is also discussed, and its connection with Hadamard matrices is highlighted. Finally, a multicomplex polar representation is provided. These properties are used to extend the standard complex baseband signal representation to the multi-dimensional case. It is shown that a set of 2 n Radio Frequency (RF) signals can be represented as the real part of a single multicomplex signal modulated by several frequencies. The signal RFs are related through a Hadamard matrix to the modulating frequencies adopted in the multicomplex baseband representation. Moreover, an orthogonal decomposition is provided for the obtained multicomplex baseband signal as a function of the complex baseband representations of the input RF signals. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 13
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 177460102
- Full Text :
- https://doi.org/10.3390/axioms13050324