Abstract
Based on quantum mechanical representation and operator theory, this paper restates the two new convolutions of fractional Fourier transform (FrFT) by making full use of the conversion relationship between two mutual conjugates: coordinate representation and momentum representation. This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics, a field that has been developing rapidly. These two new convolution methods have potential value in signal processing.
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