This paper continues the investigation in digital signal processing of spectral analysis on certain non-commutative nite groups|wreath product groups. We describe here the generalization of discrete cyclic convolution to convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group based convolution is deened in both the spatial and spectral domain...

We present a very simple and fast algorithm to compute the convolution of an arbitrary sequence x with a sequence of a specific type, a. The sequence a is any linear combination of polynomials, exponentials and trigonometric terms. The number of steps for computing the convolution depends on a certain complexity of a and not on its length, thus making it feasible to convolve a sequence with ver...

Since the introduction of the behavioral approach to systems theory by Willems [13, 14, 15, 16, 17] the main emphasis has been on discrete time systems. Papers dealing with continuous time systems generally have assumed from the start that a set of differential equations was given. In his thesis Soethoudt has given necessary and sufficient conditions on the behavior of a continuous time system ...

A Dirichlet $k$-partition of a domain is collection $k$ pairwise disjoint open subsets such that the sum their first Laplace--Dirichlet eigenvalues minimal. In this paper, we propose new relaxation problem by introducing auxiliary indicator functions domains and develop simple efficient diffusion generated method to compute $k$-partitions for arbitrary domains. The only alternates three steps: ...

Depthwise convolution and grouped convolution has been successfully applied to improve the efficiency of convolutional neural network (CNN). We suggest that these models can be considered as special cases of a generalized convolution operation, named channel local convolution(CLC), where an output channel is computed using a subset of the input channels. This definition entails computation depe...

Gaussian convolutions are perhaps the most often used image operators in low-level computer vision tasks. Surprisingly though, there are precious few articles that describe efficient and accurate implementations of these operators. In this paper we describe numerical approximations of Gaussian convolutions based on interpolation. We start with the continuous convolution integral and use an inte...

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.