New sampling theorem and multiplicative filtering in the FRFT domain
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Having in consideration a fractional convolution associated with the fractional Fourier transform (FRFT), we propose a novel reconstruction formula for bandlimited signals in the FRFT domain without using the classical Shannon theorem. This may be considered the main contribution of this work, and numerical experiments are implemented to demonstrate the effectiveness of the proposed sampling theorem. As a second goal, we also look for the designing of multiplicative filters. Indeed, we also convert the multiplicative filtering in FRFT domain to the time domain, which can be realized by fast Fourier transform. Two concrete examples are included where the use of the present results is illustrated.
KeywordsSampling theorem Multiplicative filter Signal processing Convolution Fractional Fourier transform
The authors would like to thank the editor and the anonymous referee for their valuable comments and suggestions that improved the clarity and quality of this manuscript. L.P. Castro was supported in part by FCT–Portuguese Foundation for Science and Technology through the Center for Research and Development in Mathematics and Applications (CIDMA) at Department of Mathematics of University of Aveiro, within the project UID/MAT/04106/2019. The remaining authors were partially supported by the Viet Nam National Foundation for Science and Technology Development (NAFOSTED).