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arXiv · 0907.2412

Design of Pulse Shapes Based on Sampling with Gaussian Prefilter

Edwin Hammerich
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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.

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Edwin Hammerich. 2025-08-15. Design of Pulse Shapes Based on Sampling with Gaussian Prefilter. https://doi.org/10.1109/sampta64769.2025.11133539

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