Convolution Structure of the Fractional Fourier-Laplace Transform

Vidya Sharma, Akash Patalwanshi

Abstract: Fourier related transforms have innumerous application in variety of disciplines not only in engineering sides like signal processing, optics communication but also in music, economics etc. The Fractional Fourier-Laplace transform (FrFLT) which combines the properties of both Fractional Fourier transform (FrFT) and the Laplace transform is a powerful tool in the field of signal processing and mathematical physics, which provides a better understanding of the time-frequency analysis of signals. Also convolution is a powerful way of characterizing the input output relationship of time invariant linear system. Convolution has many applications in image processing, optics, digital data processing, statistics, physics, electrical engineering, probability theory, Fractional calculus etc. In this paper, we propose the convolution structure for the Fractional Fourier-Laplace transform (FrFLT) and prove its convolution theorem.

Keywords: Fourier transform, Laplace transform, Fractional Fourier transform, Fractional Fourier-Laplace transform, signal processing

How to Cite?: Vidya Sharma, Akash Patalwanshi, "Convolution Structure of the Fractional Fourier-Laplace Transform", Volume 13 Issue 8, August 2024, International Journal of Science and Research (IJSR), Pages: 1599-1602, https://www.ijsr.net/getabstract.php?paperid=MR24827135434, DOI: https://dx.doi.org/10.21275/MR24827135434