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Sums and Products of Signals Presentation Transcript:
1.EEE223 Signals & Systems
2.Outline
Sums and products of signals
CT exponential & Sinusoidal signals
DT exponential & Sinusoidal signals
Unit impulse and unit steps signals
3.Sums & Products of Signals
Point by point addition / multiplication
Examples
4.CT Complex exponential
Ceat
In general, C and a are complex
If C, a are real => real exponential
a > 0 growing exp
a < 0 decaying exp
a = 0 constant
5.Ceat
If a is pure imaginary, then
eat = ej?t = ej?(t +T)
Periodic with period T = 2 p/ | ? |
6.CT Sinusoidal signals
x(t) = A cos ( ?ot + f )
?o = 2pfo
?o = radians per second
f = radians
fo = cycles per second (Hertz)
Euler’s relation
7.CT exponential & Sinusoidal signals
x(t) = Ceat
with C = |C| ej?
and a = r + j ?
x(t) = |C| ertej(?t+?)
x(t) = |C| ertej(?t+?)
= sinusoid * exponential envelope
8.DT exponential
x[n] = Can
In general, C and a are complex
If C, a are real => real exponential
|a| > 1 growing exp
|a| < 1 decaying exp
a < 0 oscillatory behaviour
9.DT Complex exponential
x[n] = Can
Or
x[n] = Ceßn
If ß is pure imaginary, then
x[n] = Cej?n
(Euler’s relation)
10.DT Issues:
Cej?n = Cej(?+2p)n
Frequency ? = ? + 2p SAME!!!!!!
Periodicity:
x[n+N] = x[n]
Is it true for complex exponentials?
