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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)

- David Mendlovic
- NSIP
- 1999

- Ido Raveh, David Mendlovic
- IEEE Trans. Signal Processing
- 1999

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)

There exists a fractional Fourier-transform relation between the amplitude distributions of light on two spherical surfaces of given radii and separation. The propagation of light can be viewed as a process of continual fractional Fourier transformation. As light propagates, its amplitude distribution evolves through fractional transforms of increasing… (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)

- D Mendlovic, H M Ozaktas, A W Lohmann
- Applied optics
- 1994

Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a… (More)

- D Mendlovic, H M Ozaktas, A W Lohmann
- Applied optics
- 1995

Recently, optical interpretations of the fractional-Fourier-transform operator have been introduced. On the basis of this operator the fractional correlation operator is defined in two different ways that are both consistent with the definition of conventional correlation. Fractional correlation is not always a shift-invariant operation. This property leads… (More)