On the Octonion Cross Wigner Distribution of 3-D Signals
This paper introduces definitions of the octonion cross Wigner distribution (OWD) and the octonion ambiguity function, forming a pair of octonion Fourier transforms. The main part is devoted to the study of the basic properties of the OWD. Among them are the properties concerning its nature (nonline...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/11/5358 |
| _version_ | 1827665681460494336 |
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| author | Łukasz Błaszczyk Kajetana Snopek |
| author_facet | Łukasz Błaszczyk Kajetana Snopek |
| author_sort | Łukasz Błaszczyk |
| collection | DOAJ |
| description | This paper introduces definitions of the octonion cross Wigner distribution (OWD) and the octonion ambiguity function, forming a pair of octonion Fourier transforms. The main part is devoted to the study of the basic properties of the OWD. Among them are the properties concerning its nature (nonlinearity, parity, space support conservation, marginals) and some “geometric” transformations (space shift, space scaling) similar to the case of the complex Wigner distribution. This paper also presents specific forms of the modulation property and an extended discussion about the validity of Moyal’s formula and the uncertainty principle, accompanied by new theorems and examples. The paper is illustrated with examples of 3-D separable Gaussian and Gabor signals. The concept of the application of the OWD for the analysis of multidimensional analytic signals is also proposed. The theoretical results presented in the papers are summarized, and the possibility of further research is discussed. |
| first_indexed | 2024-03-10T01:31:32Z |
| format | Article |
| id | doaj.art-4c31904c7f4343f3adc62034bcf5fe4b |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T01:31:32Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-4c31904c7f4343f3adc62034bcf5fe4b2023-11-23T13:40:18ZengMDPI AGApplied Sciences2076-34172022-05-011211535810.3390/app12115358On the Octonion Cross Wigner Distribution of 3-D SignalsŁukasz Błaszczyk0Kajetana Snopek1Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-662 Warszawa, PolandInstitute of Radioelectronics and Multimedia Technology, Warsaw University of Technology, 00-665 Warszawa, PolandThis paper introduces definitions of the octonion cross Wigner distribution (OWD) and the octonion ambiguity function, forming a pair of octonion Fourier transforms. The main part is devoted to the study of the basic properties of the OWD. Among them are the properties concerning its nature (nonlinearity, parity, space support conservation, marginals) and some “geometric” transformations (space shift, space scaling) similar to the case of the complex Wigner distribution. This paper also presents specific forms of the modulation property and an extended discussion about the validity of Moyal’s formula and the uncertainty principle, accompanied by new theorems and examples. The paper is illustrated with examples of 3-D separable Gaussian and Gabor signals. The concept of the application of the OWD for the analysis of multidimensional analytic signals is also proposed. The theoretical results presented in the papers are summarized, and the possibility of further research is discussed.https://www.mdpi.com/2076-3417/12/11/5358Wigner distributionoctonionsoctonion Fourier transform |
| spellingShingle | Łukasz Błaszczyk Kajetana Snopek On the Octonion Cross Wigner Distribution of 3-D Signals Applied Sciences Wigner distribution octonions octonion Fourier transform |
| title | On the Octonion Cross Wigner Distribution of 3-D Signals |
| title_full | On the Octonion Cross Wigner Distribution of 3-D Signals |
| title_fullStr | On the Octonion Cross Wigner Distribution of 3-D Signals |
| title_full_unstemmed | On the Octonion Cross Wigner Distribution of 3-D Signals |
| title_short | On the Octonion Cross Wigner Distribution of 3-D Signals |
| title_sort | on the octonion cross wigner distribution of 3 d signals |
| topic | Wigner distribution octonions octonion Fourier transform |
| url | https://www.mdpi.com/2076-3417/12/11/5358 |
| work_keys_str_mv | AT łukaszbłaszczyk ontheoctonioncrosswignerdistributionof3dsignals AT kajetanasnopek ontheoctonioncrosswignerdistributionof3dsignals |