Frequency Responses and Transfer Functions of Time-Invariant Discrete-Time Systems
Frequency domain techniques for time-invariant discrete-time input-output linear systems are of fairly recent vintage when compared with the corresponding continuous-time methods. Their development has taken place largely over the last fifty years, and has accelerated considerably with the advent of the computer age. Nonetheless, as is often the practice in applied mathematics, it is possible to present an overview of discrete-time frequency response techniques which is in essence completely parallel to the development in §19. Such an exposition would, however, obscure the history of the subject unnecessarily. As a result, we shall try consistently to accompany the definitions and theorems in this section with comments which should alert the reader to certain fundamental similarities and differences between continuous- and discrete-time frequency domain analysis; we shall also attempt to describe, at least briefly, how the two theories complement each other in the “real world” of systems engineering.
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