Transfer function an anticausal discrete time linear shift invariant system is given as z - 3 z² – z + 2' H(z) Sketch the given transfer function on the z-plane and obtain the impulse response of this system. Table 6.1: Some commonly used z-transform pairs. Table 6.2: Some useful properties of the z-transform.

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.16P
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Transfer function an anticausal discrete time linear shift invariant system is given
as
z - 3
z² – z + 2'
H(z) =
Sketch the given transfer function on the z-plane and obtain the impulse response of this system.
Table 6.1: Some commonly used z-transform pairs.
Table 6.2: Some useful properties of the z-transform.
Property
Sequence
z-Transform
ROC
Sequence
z-Transform
ROC
Rg
Re
g[n]
G(2)
8[n]
1
All values of z
Conjugation
Time-reversal
g*[n]
G*(?*)
Rg
1/Rg
1
gl-n]
G(1/z)
u[n]
|z| > 1
Lican ity
uglu)+ h[u]
aG(2) + pu(2)
Includes Rg n Rn
gln - no)
Rig, except possibly
the point z =0 or oo
Time-shifting
a" u[n]
|z| > la|
|-az
az-
(1 - az-l)2
Multiplication by
an exponential
na" u[n]
|z| > la|
a" g[n]
G(z/a)
sequence
dG(2)
Rg, except possibly
the point z=0 or oo
Includes Rgn Rn
(n + 1) a" u[n]
Differentiation
ngln]
(1 – az-1)2
1- (r cos w,)z-1
1 – (2r cos w,)z-1+p2z=2
(r sin wo)z-!
1- (2r cos w)z¬l+p2==2
of G(2)
dz
Convolution
gln] h[n]
G(2)H(2)
(" cos wan)u[n]
|z| > Irl
Modulation
5 fe G(v)H(z/v}u-l du
Includes RgRA
g[n]h[n]
(r" sin won)u[n]
|z| > Ir|
Transcribed Image Text:Transfer function an anticausal discrete time linear shift invariant system is given as z - 3 z² – z + 2' H(z) = Sketch the given transfer function on the z-plane and obtain the impulse response of this system. Table 6.1: Some commonly used z-transform pairs. Table 6.2: Some useful properties of the z-transform. Property Sequence z-Transform ROC Sequence z-Transform ROC Rg Re g[n] G(2) 8[n] 1 All values of z Conjugation Time-reversal g*[n] G*(?*) Rg 1/Rg 1 gl-n] G(1/z) u[n] |z| > 1 Lican ity uglu)+ h[u] aG(2) + pu(2) Includes Rg n Rn gln - no) Rig, except possibly the point z =0 or oo Time-shifting a" u[n] |z| > la| |-az az- (1 - az-l)2 Multiplication by an exponential na" u[n] |z| > la| a" g[n] G(z/a) sequence dG(2) Rg, except possibly the point z=0 or oo Includes Rgn Rn (n + 1) a" u[n] Differentiation ngln] (1 – az-1)2 1- (r cos w,)z-1 1 – (2r cos w,)z-1+p2z=2 (r sin wo)z-! 1- (2r cos w)z¬l+p2==2 of G(2) dz Convolution gln] h[n] G(2)H(2) (" cos wan)u[n] |z| > Irl Modulation 5 fe G(v)H(z/v}u-l du Includes RgRA g[n]h[n] (r" sin won)u[n] |z| > Ir|
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