313lecture2_signals - EE 313 Linear Systems and Signals...

Signals and Signal Properties
Prof. Adnan Kavak
Dept. of Electrical and Computer Engineering
The University of Texas at Austin
EE 313 Linear Systems and Signals Fall 2008

2-2
Signals
•
Signal is a set of data or information, which is a
function of an independent variable (time,
space, etc)
E.g. Phone or TV signal, monthly sales of corporation,
daily stock price, daily temperature, etc.
•
Continuous-time signals are functions of a real
argument
x ( t ) where t can take any real value
x ( t ) may be 0 for a given range of values of t
•
Discrete-time signals are functions of an
argument that takes values from a disrete set
x [ n ] where n ∈ {...-3,-2,-1,0,1,2,3...}
We sometimes use “index” instead of “time”
when discussing discrete-time signals
•
Values for x may be real or complex

2-3
Signal Energy
•
For a real-valued signal
•
For a complex-valued
signal (To make sure
that energy is real, use
magnitude square)
Measure of the signal size as the area under its amplitude square

2-4
Comment: Why do we use amplitude
square for energy?
•
Instantenous power: p(t) = i(t) * v(t)
(in general)
•
f(t) = i(t) = v(t) [ Assuming 1 Ohm resistance]
•
Then, instantenous power: p(t) = f(t) * f(t)
•
This is why we use square of the signal
amplitude (physical reason).
•
Then, energy is integral of the instantenous
power.
•
Mathematically, if we didn’t use square of
amplitude, then energy may be negative which
doesn’t make any sense.

2-5
Remarks about Signal Energy
•
Signal energy is always positive
•
Some signals (e.g. periodic) have infinite energy.