Inorder to apply a multi-dimensional linear transform over an arbitrarily shaped support, the usual practice is to ll out the support to a hypercube by zero padding. This does not however yield a satisfactory de nition for transforms in two or more dimensions. The problem that we tackle is: how do we rede ne the transform over an arbitrary shaped region suited to a given application? We present...

Abstract The general integer mapping theory of invertible linear transforms is considered in this paper. Two terms of integer factor and elementary triangular matrix are introduced. We prove that there exists an integer implementation if a linear transform is invertible and in finite dimensional space. The integer implementation of an invertible linear transform has several advantages such as (...

The correlation properties of speckle fields are studied for general paraxial systems. The previous studies on lateral and longitudinal speckle size for the case of free-space propagation (Fresnel transform) are generalized to the case of the linear canonical transform. These results have implications for the control of speckle size, through appropriate design of optical systems, with particula...

A simple lemma is derived that allows to transform a general scalar (non-Gaussian, non-additive) continuousalphabet channel as well as a general multiple-access channel into a modulo-additive noise channel. While in general the transformation is information lossy, it allows to leverage linear coding techniques and capacity results derived for networks comprised of additive Gaussian nodes to mor...

In this paper we introduce new techniques for the eecient computation of a Fourier transform on a nite group. We use the decomposition of a group into double cosets and a graph theoretic indexing scheme to derive algorithms that generalize the Cooley-Tukey FFT to arbitrary nite groups. We apply our general results to special linear groups and low rank symmetric groups, and obtain new eecient al...

Two new transforms with piecewise linear kernels are introduced. These analogues of the classical Laplace transform and Z-transform. Properties these investigated applications to ordinary differential equations integral provided. This article is ideal for study as a foundational project in an undergraduate course and/or equations.

background: epilepsy is a severe disorder of the central nervous system that predisposes  the person to recurrent seizures. fifty million people worldwide suffer from  epilepsy; after alzheimer's and stroke, it is the third widespread nervous disorder. objective: in this paper, an algorithm to detect the onset of epileptic seizures  based on the analysis of brain electrical signals (eeg) has be...

A generic ‘chirp’ of the form h(t) = A(t) cosφ(t) can be closely approximated by a connected set of multiscale chirplets with quadratically-evolving phase. The problem of finding the best approximation to a given signal using chirplets can be reduced to that of finding the path of minimum cost in a weighted, directed graph, and can be solved in polynomial time via dynamic programming. For a sig...

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the are...