EE 3120 Linear Systems Analysis
Lecture 2
Manipulation of Continuous and Discrete time Signals
reference time, the time we start to study the signal
that depends on whether you are a mathematician or an engineer
What is t = 0 ?
What is t
Æ
∞
?
Let’s consider the real exponential function:
f(t) =
e
at
for a < 0
for t
Æ
∞
,
f(t)
Æ
0
but…
for
at =
5,
f(t) =
0.007
after 5 time constants, f(t) is less than 1% of the original value at f(0) = 1.
Is this
small enough to be considered infinity?
In many controls and filter applications,
YES.
So…
if
f(t) =
e
0.1t
; f(t)
Æ
0 at 50 seconds (5 time constants);
∞
= 50 second
if
f(t) =
e
5t
;
f(t)
Æ
0 at 1 second (5 tiem constants);
∞
= 1 second
hmmm….
.
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View Full DocumentEE 3120 Linear Systems Analysis
Lecture 2
Manipulation of Continuous and Discrete time Signals
Positive time signals
f(t) = 0
for t < 0
f(t) = f
+
(t)
Negative time signals
f(t) = 0
for t > 0
f(t) = f

(t)
2sided signals
f(t)
≠
0
for any t < 0 and t > 0
Most signals in practice are positive time signals.
Boundedness
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 Fall '08
 ARAVENA
 Digital Signal Processing, Signal Processing, Discrete Time Signals, Linear Systems Analysis

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