It was shown [ 21 that any SFF can be decomposed in this manner. Thus, F(x) is an SFF if, and only if, it can be expressed as the sum of four functions in the form of the above equation. Additional SFF studies are reported in refs. [ 3-51. Another issue that has been recently investigated is the fractional Fourier transform [ 6-91. Two distinct definitions of the fractional Fourier transform ha...

Keywords: fractal geometry, fractional derivative, fractional Fourier transform, fractional power of a matrix, self similarity, complex partial differential equation, broadband ultrasound, frequency-dependent attenuation, time domain. 1. Backgrounds The rational behind this model is schematically illustrated below: Fractal geometry (irregular soft tissues) → Fractional Fourier transform (freque...

In this paper, a new tool that is fractional Fourier Transform is introduced to 3D model retrieval. And we propose a 3D model descriptor based on 3D factional Fourier transform. Fractional Fourier transform is a general format of Fourier transform, and add a variables that is order. Our approach is based on volume. The first step of the approach is that voxelize these 3D models. A coarse voxeli...

The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to the Gouy phase shift between the two surfaces. This result provides new insight into wave propagation and spherical mirror resonators as well as the possibility of exploiting ...

Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics configuration for performing the fractional-Fourier-transform operation [J. Opt. Soc. Am. A 10, 2181 (1993)] provides a scaled output using a fixed lens. For obtaining a non-scaled...

An efficient method for implementing closed form discrete fractional Fourier transform for the purpose of signal compression is presented. Implementation method is compared with that of existing closed form discrete fractional Fourier transform, with respect to computational complexity, variance of quantization error, signal to noise ratio and number of bits for the representation of coefficien...

An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N , the presented algorithm computes the fractional transform in O( N log N ) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed.

An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N , the presented algorithm computes the fractional transform in O( N log N ) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed.

We present much briefer and more direct and transparent derivations of some sampling and series expansion relations for fractional Fourier and other transforms. In addition to the fractional Fourier transform, the method can also be applied to the Fresnel, Hartley, and scale transform and other relatives of the Fourier transform. ? 2003 Published by Elsevier B.V.

--The fractional fourier transform(FRFT) which is a generalisation of classical fourier transform, was introduced number of years ago in the mathematics literature but appears to have remained largely unknown to a signal processing community to which it may, however, be a potentially useful. The fractional fourier transform depends on a parameter ‘α’ and can be interpreted as a rotation by an a...