Algebraic Signal Processing Theory: Foundation and 1-D Time

This paper introduces a general and axiomatic approach to linear signal processing (SP) that we refer to as the algebraic signal processing theory (ASP). Basic to ASP is the linear signal model defined as a triple (A, M, ) where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively. The mapping generalizes the concept of a z-transform to bijective linear mappings from a vector space of signal samples into the module M. Common concepts like filtering, spectrum, or Fourier transform have their equivalent counterparts in ASP. Once these concepts and their properties are defined and understood in the context of ASP, they remain true and apply to specific instantiations of the ASP signal model. For example, to develop signal processing theories for infinite and finite discrete time signals, for infinite or finite discrete space signals, or for multidimensional signals, we need only to instantiate the signal model to one that make...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Markus Püschel, José M. F. Moura
• Keywords: ASP Signal Model, Signal Models, Space, TSP 2008