Frequency response of linear time periodic systems

A frequency response for linear time periodic (LTP) systems that exploits the one-to-one map induced by geometrically periodic signals is developed. This map is described by an integral operator, based on the GP (geometrically periodic) test input, and a generalized harmonic balance approach, based on an EMP (exponentially modulated periodic) input. The singular values or principal gains of the LTP operator are discussed, and the LTP principal gain diagram is described. Directional properties of the LTP operator are discussed, and notions of the domain and range spaces are presented. The framework of linear operators described has lead to the development of a comprehensive open-loop analysis theory for LTP systems, including a characterization of poles, transmission zeros, and their directional properties.<
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