Approximating the finite Mellin and Sumudu transforms utilizing wavelet transform

Classical Wavelet Transforms over Finite Fields

This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...

Wavelet Filtering with the Mellin Transform

It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters (system functions) and scale filters (multiplication operators in the scale domain), subject to the convergence of the defining integrals. The usual wavelet recons...

A note on the comparison between Laplace and Sumudu transforms

Mellin Transforms and Asymptotics: Finite Differences and Rice's Integrals

High order differences of simple number sequences may be analysed asymptotically by means of integral representations, residue calculus, and contour integration. This technique, akin to Mellin transform asymptotics, is put in perspective and illustrated by means of several examples related to combinatorics and the analysis of algorithms like digital tries, digital search trees, quadtrees, and d...

classical wavelet transforms over finite fields

this article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. we present a concrete formulation for the frobenius norm of the classical wavelet transforms over finite fields. it is shown that each vector defined over a finite field can be represented as...