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, 2-D pictures {x,y}, 3-D 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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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
x
t dt
∞
−∞
=
∫
Signal Energy
2
( )
x
E
x t
dt
∞
−∞
=
∫
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.