Optical transformation from chirplet to fractional Fourier transformation kernel

TL;DR

This paper introduces a novel optical transformation that converts chirplet functions into fractional Fourier transformation kernels, revealing new relationships in phase space and quantum correspondence, with properties like invertibility and adherence to Parseval's theorem.

Contribution

The paper presents a new invertible integration transformation connecting chirplet functions to fractional Fourier kernels, expanding the understanding of phase space and quantum operator relationships.

Findings

Transformation is invertible and obeys Parseval's theorem.

Reveals a new relationship between phase space functions and quantum operators.

Enables conversion from chirplet to fractional Fourier kernel.

Abstract

We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship between a phase space function and its Weyl-Wigner quantum correspondence operator is revealed.