Design of Pulse Shapes and Digital Filters Based on Gaussian Functions

Abstract: Two new pulse shapes for communications are presented. The first pulse shape is ISI-free and identical with the interpolating function (or ISI-free kernel) of a reconstruction formula in shift-invariant spaces with Gaussian generator. Several closed form representations in time and frequency domain are given including one for an approximation that is particularly simple. The second pulse shape is the root of the former and obtained by spectral factorization. As a consequence, shifted versions of it form an orthonormal system in the Hilbert space of finite-energy signals. The latter pulse shape is described as the response of an infinite-order digital FIR filter on a Gaussian function as input signal. Several equivalent versions of the digital filter including their finite-order approximations are presented. All filters enjoy the property that explicit formulas for their coefficients and poles are available. The filters are fully parametrizable with respect to bandwidth and sampling rate of the digital data.