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...
We introduce some new models of infinite-state transition systems. The basic model, called a (reversal-bounded) counter machine (CM), is a nondeterministic finite automaton augment...
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 ...
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 d...
A special final coalgebra theorem, in the style of Aczel's [2], is proved within standard Zermelo-Fraenkel set theory. Aczel's AntiFoundation Axiom is replaced by a varia...