4.9Frequency Response of Discrete-Time Systems
By now, it should be apparent that the methods for describing and analyzing the behavior of LTI continuous-time and discrete-time systems are similar. Indeed, both types of systems possess a natural response, independent of the system’s input (or inputs), and similar in form to the impulse response of the system. The impulse response and the system transfer function form a Laplace transform pair for continuous-time systems and a z-transform pair in the case of discrete-time systems. The forced response of each is expressible by convolution, an integral for continuous-time systems and a sum for discrete-time systems.
BIBO stable systems are characterized by the location of transfer function poles ...
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