A study of an inverse system's existence for periodic signals

摘要

Generally there isn't a stable inverse system of a linear time-invariant system with non-minimum phases. Also an inverse system of a FIR system with minimum phases is generally an IIR system. This paper describes that an inverse FIR system of a FIR system exists on condition that input-signals are periodic. The studied periodic signals are two: simple periodic signals and symmetrical periodic signals. The condition for the existence of the inverse system is studied in the frequency domain and the filter matrix expression.