A new convolution theorem associated with the linear canonical transform
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In this paper, we first introduce a new notion of canonical convolution operator, and show that it satisfies the commutative, associative, and distributive properties, which may be quite useful in signal processing. Moreover, it is proved that the generalized convolution theorem and generalized Young’s inequality are also hold for the new canonical convolution operator associated with the LCT. Finally, we investigate the sufficient and necessary conditions for solving a class of convolution equations associated with the LCT.
KeywordsConvolution operator Convolution theorem Linear canonical transform Young’s inequality Convolution equations
The author thanks the referees very much for carefully reading the paper and for elaborate and valuable suggestions.
- 1.Anh, P.K., Castro, L.P., Thao, P.T., Tuan, N.M.: Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights. In: AIP Conference Proceedings, Volume 1798, pp. 020006. AIP Publishing, Melville (2017)Google Scholar
- 10.Ozaktas, H.M., Zalevsky, Z., Kutay, M.A.: The Fractional Fourier Transform. Wiley, New York (2001)Google Scholar
- 17.Stern, A.: Why is the linear canonical transform so little known? In: AIP Conference Proceedings, 5’th International Workshop on Information Optics, vol. 860, pp. 225–234Google Scholar