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The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized(More)
Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Several mathematical properties are derived. It is often the case that an operation(More)
A new, to our knowledge, iterative algorithm for achieving optimization of beam profiles in a three-dimensional volume is presented. The algorithm is based on examining the region of interest at discrete plane locations perpendicular to the propagation direction. At each such plane an intensity constraint is imposed within a well-defined transverse spatial(More)
In this communication we propose performing two-dimensional correlation operation between phase-space representations based on the fractional Fourier transform, instead of correlating the signals themselves. A numerical examples clearly indicates superior discrimination performance. Ó 2001 Published by Elsevier Science B.V.
A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing(More)
Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a= 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Fractional Fourier transforms can extend the range of spatial filtering operations. The(More)