Algebraic Signal Processing Theory: 1-D Space

In our paper titled "Algebraic Signal Processing Theory: Foundation and 1-D Time" appearing in this issue of the IEEE TRANSACTIONS ON SIGNAL PROCESSING, we presented the algebraic signal processing theory, an axiomatic and general framework for linear signal processing. The basic concept in this theory is the signal model defined as the triple ( 8), where is a chosen algebra of filters, an associated -module of signals, and 8 is a generalization of the -transform. Each signal model has its own associated set of basic SP concepts, including filtering, spectrum, and Fourier transform. Examples include infinite and finite discrete time where these notions take their well-known forms. In this paper, we use the algebraic theory to develop infinite and finite space signal models. These models are based on a symmetric space shift operator, which is distinct from the standard time shift. We present the space signal processing concepts of filtering or convolution, " -transform,&q...

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