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.