—We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes… (More)
—We are concerned with the problem of optimally measuring an accessible signal under a total cost constraint, in order to estimate a signal which is not directly accessible. An important aspect of our formulation is the inclusion of a measurement device model where each device has a cost depending on the number of amplitude levels that the device can… (More)
We show that there is a limit to the total number of bits per second , B, of information that can flow in a simple digital electrical interconnection that is set only by the ratio of the length l of the interconnection to the total cross-sectional dimension p A A A of the interconnect wiring—the " aspect ratio " of the interconnection. This limit is largely… (More)
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… (More)
—We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation , and scaling operations. The… (More)
It is customary to define the time-frequency plane such that time and frequency are mutually orthogonal coordinates. Representations of a signal in these domains are related by the Fourier transform. We consider a continuum of " fractional " domains making arbitrary angles with the time and frequency domains. Representations in these domains are related by… (More)
A new IIR Nyquist filter with zero intersymbol interference and its frequency response approximation, " IEEE Trans. , " Recursive Nth-band digital filters—Part II: Design of multistage decimators and interpolators, " IEEE Trans. Abstract— Filtering in a single time domain or in a single frequency domain has recently been generalized to filtering in a single… (More)
We introduce the fractional Fourier domain decomposition. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems. 1999 Published by Elsevier Science B.V. All rights reserved.