A new convolution operator for the linear canonical transform with applications
| Autor: | Luis P. Castro, A. S. Silva, Navdeep Goel |
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| Rok vydání: | 2021 |
| Předmět: |
Signal processing
Applied Mathematics Multiplicative function 020206 networking & telecommunications 02 engineering and technology Type (model theory) Integral equation Convolution Domain (mathematical analysis) Linear canonical transform Computational Mathematics Product (mathematics) 0202 electrical engineering electronic engineering information engineering Applied mathematics 020201 artificial intelligence & image processing Time domain Filtering Integral equations Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 1807-0302 2238-3603 |
| DOI: | 10.1007/s40314-021-01484-9 |
| Popis: | The linear canonical transform plays an important role in engineering and many applied fields, as it is the case of optics and signal processing. In this paper, a new convolution for the linear canonical transform is proposed and a corresponding product theorem is deduced. It is also proved a generalized Young's inequality for the introduced convolution operator. Moreover, necessary and sufficient conditions are obtained for the solvability of a class of convolution type integral equations associated with the linear canonical transform. Finally, the obtained results are implemented in multiplicative filters design, through the product in both the linear canonical transform domain and the time domain, where specific computations and comparisons are exposed. Fundação para a Ciência e Tecnologia published |
| Databáze: | OpenAIRE |
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