EXAMPLES: 2-TRANSFORM HW: x[n] = 28[n] + 38[n-1] + 58[n- 2] + 28[n- 3] Region of Line No. x(m), niz0 z-Transform M:) Convergence 1 xn) 2 le >0 3 1- 4 (2- 1) d'u(n) e| > lal 7 E| > la) (:- ay z sin (a) - 2z cos (a) +1 :- cos (a)) - 2z cos (a) +1 [a sin (b)): - 2a cos(b): + a :- a cos (b)| - 2a cos (b): + a-? sin (b): 9 10 cos(an)u(n) d'sin (hn)u(n) e| > la| 12 d' cos(bn)udn) 13 sin (hn)udn) 1:- cos (b) - 12e cos (bil:+e 14 cos (bnju(n) %3D

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EXAMPLES: 2-TRANSFORM
HW:
x[n] = 28[n] + 38[n-1]+58[n-2] + 28[n- 3]
Line No. x(n), niz0
Region of
Convergence
z-Transform X(:)
x(n)
8(n)
2 >0
az
3
au(n)
4
nu(n)
E > 1
d'un)
|z| > lal
7
8
na"uk n)
E > la)
(:
z sin (a)
22- 2z cos (a) + 1
:- cos (a))
2z cos (a) +1
[a sin (b)):
-(2a cos (b)): + a
: -a cos (b)]
2- (2a cos (b)]: + a
[e sin (b))
12 cos (b)): +e
1: - e" cos (b)I
- 12e cos (bl: +e 2a
- a)
sin(a)udn)
10
cos (an)u(n)
l2 > 1
11
d' sin (hn)u(n)
| > la|
d' cos (bn)ukn)
El > lal
12
ean sin (bn)udn)
El >
13
14
"cos (bn)u(n)
Page 4|4
%3D
Transcribed Image Text:EXAMPLES: 2-TRANSFORM HW: x[n] = 28[n] + 38[n-1]+58[n-2] + 28[n- 3] Line No. x(n), niz0 Region of Convergence z-Transform X(:) x(n) 8(n) 2 >0 az 3 au(n) 4 nu(n) E > 1 d'un) |z| > lal 7 8 na"uk n) E > la) (: z sin (a) 22- 2z cos (a) + 1 :- cos (a)) 2z cos (a) +1 [a sin (b)): -(2a cos (b)): + a : -a cos (b)] 2- (2a cos (b)]: + a [e sin (b)) 12 cos (b)): +e 1: - e" cos (b)I - 12e cos (bl: +e 2a - a) sin(a)udn) 10 cos (an)u(n) l2 > 1 11 d' sin (hn)u(n) | > la| d' cos (bn)ukn) El > lal 12 ean sin (bn)udn) El > 13 14 "cos (bn)u(n) Page 4|4 %3D
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