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1
Lecture #7 EGR 261
–
Signals and Systems
Signals and Systems
Signals
A signal is a set of data or information. Examples include cell phone signals, television signals, voltages or currents in circuits, etc. The signals that we consider in this course are functions of the independent variable time, but our discussions would apply equally well to signals of other independent variables. Some examples of signals are shown below.
Read:
Ch. 1, Sect. 1-4, 6-8 in
Linear Signals & Systems, 2
nd
Ed.
by Lathi Sound segment
t [s] v(t) [V] 20 2 4 6 8 10 12 0 0
Voltage ramp waveform
2
Lecture #7 EGR 261
–
Signals and Systems
Systems
A system is any process that results in the transformation of signals. A system might have an input signal x(t) and an output signal y(t) as shown below. A system may be made up of physical components, such as in electric circuits or mechanical systems, or a system may be a software algorithm that modifies a signal.
System
Input signal = x(t) y(t) = Output signal Continuous-time system
Signal Energy and Signal Power
Two useful measures of the “size” of a signal are
signal energy and signal power.
3
Lecture #7 EGR 261
–
Signals and Systems
Signal Energy
Signal energy, E
x
, is defined as the area under x
2
(t). For example, signal energy for f(t) shown below is the shaded area shown under f
2
(t). E
x
is defined mathematically as follows:
-2x-2x
signals)valued-complex(for dt x(t)E
signals)real(for (t)dt xE
or
4
Lecture #7 EGR 261
–
Signals and Systems
Signal Power
Signal energy must be finite in order for it to be a meaningful measure of signal size. If energy is to be finite, then the signal amplitude must decay, or it is required that signal energy
0 as |t|
so that the integral will converge. When signal energy is infinite, a more meaningful measure of the size of a signal is power. Signal power, P
x
, is the time average of the energy. P
x
is defined mathematically as follows:
T/2T/2-2TxT/2T/2-2Tx
signals)valued-complex(for dt x(t)
T1 limPsignals)real(for (t)dt x
T1 limP
or
T/2T/2-2xT/2T/2-2x
signals) periodicvalued-complex(for dt x(t)
T1 Psignals) periodicreal(for (t)dt x
T1 P
or
For periodic signals with period T, P
x
is defined as:

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