Convolution is one of the most widely used digital signal processing operations. It can be implemented using the fast Fourier transform (FFT), with a computational complexity ofO(N logN). The undecimated discrete wavelet transform (UDWT) is linear and shift invariant, so it can also be used to implement convolution. In this paper, we propose a scheme to implement the convolution using the UDWT,...

In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.

1. Introduction 2. Order and type in classical complex analysis 3. Relative order and type of convex functions 4. Order and type in duality 5. The infimal convolution 6. The order of an entire function 7. A geometric characterisation of the relative order 8. An extension problem for holomorphic functions 9. Whittaker's decomposition theorem 10. Inequalities for the infimal convolution 11. Inequ...

The infimal convolution of M-convex functions is M-convex. This is a fundamental fact in discrete convex analysis that is often useful in its application to mathematical economics and game theory. M-convexity and its variant called M-convexity are closely related to gross substitutability, and the infimal convolution operation corresponds to an aggregation. This note provides a succinct descrip...

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classica...

In this paper, we present an implementation of a real-time convolver, based on Field Programmable Gate Arrays (FPGA’s) to perform the convolution operations. Main characteristics of the proposed approach are the usage of external memory to implement a FIFO buffer where incoming pixels are stored and the partitioning of the convolution matrix among several FPGA’s, in order to allow data-parallel...

The performance of MMSE Iterative Equalization based on MAP-SBVP and COD-MAP algorithms (for generating extrinsic information) are compared for fading and non-fading communication channels employing serial concatenated convolution codes. MAP-SBVP is a convolution decoder using a conventional softMAP decoder followed by a soft-convolution encoder using the soft-boolean value propagation (SBVP). ...

In 9] Knuth shows how to derive the convolution formulas of Ha-gen, Rothe and Abel from Vandermonde's convolution or binomial theorem for integer exponents. In the present paper, we shall rst present a short and elementary proof of the multi-extension of the above con-volution formulas, due to Raney and Mohanty. In the second part we shall present a multi-version of Knuth's approach to convolut...

The International Commission on Radiation Units and Measurements Report 62 (ICRU 1999) introduced the concept of expanding the clinical target volume (CTV) to form the planning target volume by a two-step process. The first step is adding a clinically definable internal margin, which produces an internal target volume that accounts for the size, shape and position of the CTV in relation to anat...