Improved computation in terms of accuracy and speed of LTI system response with arbitrary input

Abstract

Spectral analysis and system identification techniques require suitably long data sets. Linear time-invariant (LTI) systems under random input can be demanding in terms of accurate simulation of all dynamics because of calculation time. This paper details an extension of the state-space formulation of LTI systems for higher order holds, for periodic and for exponential inputs. Exact solutions of the differential state equation are implemented into loops computing only matrix-vector multiplications. The algorithmic complexity is compared to other ordinary differential equations solvers. The presented methods can be applied to arbitrary inputs. In particular, it is shown that long system responses under random input can be computed efficiently and accurately in the time and frequency domains.