Design of Pulse Shapes Based on Sampling with Gaussian Prefilter

TL;DR

This paper introduces two novel pulse shapes for communication systems, one ISI-free and the other orthonormal, both based on Gaussian prefilter sampling, enhancing signal processing capabilities.

Contribution

The paper presents new pulse shapes derived from Gaussian prefilter sampling, including an ISI-free pulse and an orthonormal pulse, with specific decay properties and applications.

Findings

First pulse shape is ISI-free and similar to sinc near origin

Second pulse shape has superexponential decay and is orthonormal

Both pulse shapes are suitable for improved communication signal processing

Abstract

Two new pulse shapes for communications are presented. The first pulse shape generates a set of pulses without intersymbol interference (ISI) or ISI-free for short. In the neighborhood of the origin it is similar in shape to the classical cardinal sine function but is of exponential decay at infinity. This pulse shape is identical to the interpolating function of a generalized sampling theorem with Gaussian prefilter. The second pulse shape is obtained from the first pulse shape by spectral factorization. Besides being also of exponential decay at infinity, it has a causal appearance since it is of superexponential decay for negative times. It is closely related to the orthonormal generating function considered earlier by Unser in the context of shift-invariant spaces. This pulse shape is not ISI-free but it generates a set of orthonormal pulses. The second pulse shape may also be used to define a receive matched filter so that at the filter output the ISI-free pulses of the first kind are recovered.