The Statistical Properties Of Filtered Signals
Ephraim Gower, T. Tsalaile, Monageng Kgwadi, Malcolm J. Hawksford · Zenodo (CERN European Organization for Nuclear Research) · 2013
In this paper, the statistical properties of filtered or convolved signals are considered by deriving the resulting density functions as well as the exact mean and variance expressions given a prior knowledge about the statistics of the individual signals in the filtering or convolution process. It is shown that the density function after linear convolution is a mixture density, where the number of density components is equal to the number of observations of the shortest signal. For circular convolution, the observed samples are characterized by a single density function, which is a sum of products.