%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