Design of pulse shapes based on sampling with Gaussian prefilter

Edwin Hammerich

Session: General

Keywords: pulse shape, sampling, Gaussian prefilter

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.

Submission Number: 30