Discrete-Time Signals and Systems

Discrete-time signals are obtained by the sampling of continuous-time signals. Digital signal processing deals basically with discrete-time signals, which are processed by discrete-time systems. The characterization of discrete-time signals as well as discrete-time systems in time domain is required to understand the theory of digital signal processing. In this chapter, time-domain sampling and the fundamental concepts of discrete-time signals as well as discrete-time systems are considered. First, the sampling process of analog signals is described. Next, the basic sequences of discrete-time systems and their classification are emphasized. The input-output characterization of linear time-invariant (LTI) systems by means of convolution sum is described. Further, sampling of discrete-time signals is introduced. Finally, the state-space representation of discrete-time LTI systems is described.