Lecture 2: Frequency Response
Continuous time with transfer function : . An analogous result holds for discrete time systems.
Let the input to a discrete-time system be
(everlasting, so we don't have to worry about transients). Then
More particularly, consider when . We find that
or, in polar form with we find
That is, the cosine is modified in amplitude and phase by the transfer function.
Note that is periodic.