Abstract
The shift-invariant spaces act as a crucial roll in signal processing and multiresolution analysis. With the linear canonical transform (LCT) has attracted much attention in signal processing, the researches of the shift-invariant spaces for the LCT have been studied in some literature. However, these results are still related to the traditional Fourier transform (FT), which leads to the limitations for processing non-stationary signals. To overcome these shortcomings, in this paper, the new definition of shift-invariant spaces associated with the LCT and their applications have been presented. First, by applying the classical LCT convolution theorem, the new shift-invariant spaces for the LCT have been developed. Subsequently, by utilizing the new definition, the typical uniform sampling, the sampling using arbitrary basis functions, and the non-ideal sampling for the LCT have been presented. In addition, as another important application, the fractional delay filters for the LCT have also been studied. Finally, the simulations have been presented to show the effectiveness and correctness of the developed theorems.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
