Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

doi:10.1088/1674-1056/19/7/074201

Abstract Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional-order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.

Keywords: chirp transform Fresnel diffraction Wigner distribution function fractional Fourier transform

Received: 31 August 2009
Revised: 14 December 2009
Accepted manuscript online:

PACS:	42.60.Fc	(Modulation, tuning, and mode locking)
	02.50.Ng	(Distribution theory and Monte Carlo studies)
	02.30.Uu	(Integral transforms)
	02.60.Nm	(Integral and integrodifferential equations)

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Shi Peng(石鹏) , Cao Guo-Wei(曹国威), and Li Yong-Ping(李永平) Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform 2010 Chin. Phys. B 19 074201

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Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

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