10-10-2012, 12:31 PM
Theory and Problems of Signals and Systems
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Signals and Systems
INTRODUCTION
The concept and theory of signals and systems are needed in almost all electrical
engineering fields and in many other engineering and scientific disciplines as well. In this
chapter we introduce the mathematical description and representation of signals and
systems and their classifications. We also define several important basic signals essential to
our studies.
SIGNALS AND CLASSIFICATION OF SIGNALS
A signal is a function representing a physical quantity or variable, and typically it
contains information about the behavior or nature of the phenomenon. For instance, in a
RC circuit the signal may represent the voltage across the capacitor or the current flowing
in the resistor. Mathematically, a signal is represented as a function of an independent
variable t. Usually t represents time. Thus, a signal is denoted by x(t).
Analog and Digital Signals:
If a continuous-time signal x(l) can take on any value in the continuous interval (a, b),
where a may be - 03 and b may be + m, then the continuous-time signal x(t) is called an
analog signal. If a discrete-time signal x[n] can take on only a finite number of distinct
values, then we call this signal a digital signal.
Basic Properties:
Most of the properties of the unilateral z-transform are the same as for the bilateral
z-transform. The unilateral z-transform is useful for calculating the response of a causal
system to a causal input when the system is described by a linear constant-coefficient
difference equation with nonzero initial conditions. The basic property of the unilateral
z-transform that is useful in this application is the following time-shifting property which is
different from that of the bilateral transform.