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Linear Systems and Signals
Lecture 1
Introduction to signals and systems
Signals: single valued functions that carry information (e.g. voice, radar,
control, heart EKG, brainwaves, 2D pictures {x,y}, 3D video
or RF electromagnetic radiation
{x,y,t})
Systems: perform some kind of manipulation (processing) of signals
(e.g.
microphone, speaker, amplifier, demodulator)
Systems
can be electrical, mechanical, hydraulic, etc.
Continuous time signals
– signals defined at every instant in time. Usually
denoted f(t) for all t (
∞
,
∞
).
In reality, no signal starts from 
∞
and lasts forever
but it is convenient to represent
signals this way.
Discrete time signals
– signals defined only at discrete instants of time,
but have a continuous range of amplitudes
Digital signals
– discrete time signals with discrete (quantized) amplitudes
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View Full Document Size of a Signal
Many times engineers are interested in quantifying a signal.
The two most common
ways of quantifying a signal is by computing the
signal energy
and
signal power.
2
()
x
E
xtd
t
∞
−∞
=
∫
Signal Energy
2
x
Ex
t
d
t
∞
−∞
=
∫
Generalized for complex signals:
Defined as the area under squared signal, or the magnitude squared area.
This is only a meaningful measure of the signal size if it is finite.
These integrals will be
finite only if the signal amplitude
Æ
0 as t
Æ
infinity.
If a signal amplitude does not eventually decay to zero, then the signal energy is infinite
and the signal is NOT an energy signal.
Size of a Signal
If the signal energy is infinite, we can calculate another measure of the signal, the time
average of the energy, or the
power of the signal.
2
2
2
1
lim
( )
T
x
T
T
P
xtd
t
T
→∞
−
=
∫
Signal Power
2
2
2
1
lim
( )
T
x
T
T
P
xt
d
t
T
−
=
∫
Generalized for complex signals:
The signal power is the time average or mean of the signal amplitude squared.
The
square root of this signal power is the rootmeansquared, or RMS of a signal.
The signal power can be found as long as the signal is periodic, otherwise the average
may not exist.
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View Full DocumentThe energy calculated does not indicate the actual energy signal because the energy
also depends on the load.
We can interpret the measurement as the
energy dissipated
across a normalized load of a 1ohm resistor.
x(t)
1 ohm
A real signal source consists of an
independent voltage source and a
series resistance.
The energy delivered to
R2 depends on R1 and R2 through
voltage division.
We use the normalization to represent
the maximum energy capability.
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This note was uploaded on 02/06/2012 for the course EE 2120 taught by Professor Aravena during the Fall '08 term at LSU.
 Fall '08
 ARAVENA
 Electromagnet

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