Shift Operator and Separation Filter for Different Period Mixed Signals Using Companion Matrix

In this paper, we present a novel operator designed to handle the shifting of multiple periodic signals. By exploiting the unique properties of the companion matrix and the elegant structure of cyclotomic polynomials, we have developed an efficient and versatile tool for signal processing applications. The proposed operator can be further utilized to design an FIR filter for decomposition and separation of different period mixed signals.