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

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 all dynamics because calculation time. This paper details an extension the state-space formulation LTI for higher order holds, periodic exponential inputs. Exact solutions differential state equation are implemented into loops computing only matrix-vector multiplications. The algorithmic complexity is compared to other ordinary equations solvers. presented methods applied arbitrary In particular, it shown that responses computed efficiently accurately time frequency domains.