Algebraic Signal Processing Theory

In [1], 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 (A, M, ), where A is a chosen algebra of filters, M an associated A-module of signals, and is a generalization of the z-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, "z-transform," spectrum, and Fourier transform. For finite length space signals, we obtain 16 variants of space models, which have the 16 discrete cosine and...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Markus Püschel, José M. F. Moura
• Keywords: CORR 2006, Education, Linear Signal Processing, Signal Models, Space Signal