  In this paper we show that the knowledge of noise statistics contaminating a
signal can be effectively used to choose an optimal Gaussian filter to
eliminate noise. Very specifically, we show that the additive white Gaussian
noise (AWGN) contaminating a signal can be filtered best by using a Gaussian
filter of specific characteristics. The design of the Gaussian filter bears
relationship with the noise statistics and also some basic information about
the signal. We first derive a relationship between the properties of the
Gaussian filter, noise statistics and the signal and later show through
experiments that this relationship can be used effectively to identify the
optimal Gaussian filter that can effectively filter noise.
