Generalized Frequency Response Concepts for Time-Varying, Discrete-Time Linear Systems

It is shown that many of the frequency response concepts associated with time-invariant linear systems can be extended in a meaningful manner to time-varying, discrete-time linear systems. Generalized frequency domain representations of the input and output are introduced along with a generalized frequency response or transfer function relating input and output. In addition, generalizations of bandwidth, gain bandwidth product, and Parseval´s (Plancherel´s) theorem are introduced. The key to these developments is the use of a decomposition of the system matrix based on its singular values.