  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.
