%0 Journal Article %A Ephraim Gower and Thato Tsalaile and Monageng Kgwadi and Malcolm Hawksford. %D 2013 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 77, 2013 %T The Statistical Properties of Filtered Signals %U https://publications.waset.org/pdf/16758 %V 77 %X 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. %P 875 - 878