Some generalization of discrete convolution

Bohdan S. Butkiewicz

doi:10.1117/12.871989

14 September 2010 Some generalization of discrete convolution

Bohdan S. Butkiewicz

Proceedings Volume 7745, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2010; 77451L (2010) https://doi.org/10.1117/12.871989
Event: Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2010, 2010, Wilga, Poland

Abstract

Conventional discrete convolution is defined as sum of product of two components, where one is shifted in time. In the paper the product is replaced by other operations called triangular norms. The algebraic product is a member of this family of operations. Therefore, such convolution is generalization of conventional convolution. This approach leads to nonlinear operations. Thus, such idea represents a concept of nonlinear filtering. It was shown that such filters has identical impulse, step, and frequency responses as conventional one. However, they are nonlinear filters and of course responses to an input signal can be different for conventional and such filters. Some other properties of these filters are investigated and compared.

Citation Download Citation

Bohdan S. Butkiewicz "Some generalization of discrete convolution", Proc. SPIE 7745, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2010, 77451L (14 September 2010); https://doi.org/10.1117/12.871989

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