Optical transformation from chirplet to fractional Fourier transformation kernel

2009/02/11 by Hong-yi Fan, Li-yun Hu · 1 citation
Mathematics · Physics and Astronomy · #Fourier transform #Invertible matrix #Kernel (algebra) #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Operator (biology) #Orbital Angular Momentum in Optics #Parseval's theorem #Phase (matter) #Space (punctuation) #Transformation (genetics) #quant-ph

paper · pdf · doi:10.1080/09500340903033690

3 pages, no figure

arxiv created 2009/02/11 · openalex publication_date 2009/06/20 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We find a new integration transformation which can convert a chirplet function to a 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.

Citations

• Quantenmechanik und Gruppentheorie
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. I. Mapping Theorems and Ordering of Functions of Noncommuting Operators
• On the Quantum Correction For Thermodynamic Equilibrium

Cited by

• Fractional Fourier transform [wikipedia]

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