On hyperbolic complex LTI digital systems

An investigation of digital systems based on hyperbolic (complex) numbers is presented for the first time. We consider the algebra of hyperbolic numbers (i.e. complex numbers possessing the imaginary j² = 1) as the simplest instance of a non-division algebra, which allows us to examine the impact of zero divisors in the case of DSP applications. As an example, the analysis of a general first order hyperbolic system is presented.