Chapter 1 Fundamental Concepts.ppt

§1-1 Introduction
Chapter 1 Fundamental Concepts
§1-2 Discrete-Time Signals
§1-3 Discrete-time Systems
§1-4 Basic Properties of Discrete-time Systems
Problems
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§1-1 Introduction
The concepts of signals and systems arise in virtually all areas of technology, ranging from appliances or devices found in homes to very sophisticated engineering innovations. In fact, it can be argued that much of the development of high technology is a result of advancements in the theory and techniques of signals and systems.
Last term, in the course of signals and systems, we have studied the continuous-time system analysis. In this term, we are going to study the discrete-time system analysis. Let us begin with the fundamental concepts of the discrete-time system analysis.
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§1-2 Discrete-Time Signals
Definitions:
Discrete-time variable: The time variable t is said to be a discrete time variable if t takes on only the discrete values t=tn for some range of integer values of n.
Discrete-time signals: A discrete-time signal is a signal that is a function of the discrete time variable tn, denoted with x(tn), where x(t) is a continuous-time signal.
The resulting discrete-time signal x(tn) is called the sampled version of the original continuous-time signal x(t).
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Let tn=nT, where T is called the sampling interval. If T is a constant, the sampling process is called uniform sampling, otherwise, nonuniform sampling. Note that the nonuniform sampling is sometimes used in applications but is not considered in this course. So, we often use x[n] to denote x(tn), .,
x[n]= x(tn)= x(t)|t=nT= x(nT)
Also note that the square brackets instead of parentheses are used to denote the discrete-time signal x[n].
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For example,
where T=1/15, n=0, 1, 2, …, 30. The plots of x[n] and x(t) are given in Fig. 1-1
Fig. 1-1
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Typical and Simple Examples of Discrete-Time Signals
Discrete-time Unit-step Function u[n]
Definition:
The plot of u[n] is shown in Fig. 1-2
Fig. 1-2
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Discrete-