Transforms and its Applications: UNIT 2: Z Transform
Z Transform: First Shifting theorem (Frequency shifting)
Z Transform: Example Important Solved Problems with formula, steps, derivation and answer based on Z Transform: First Shifting theorem (Frequency shifting), Damping rule.
First Shifting theorem [Frequency shifting]:
Damping rule
[The geometric factor a‒n when |a| <
1, damps the function un. Hence we use the name damping rule]
(i)
If Z {f(n)} = F(z), then Z {an f(n)}
= F [ z/a ]
(ii)
If Z {f(n)} = F(z), then Z [a‒nf(n)]
= F [az]
Proof:
Problems based on first shifting theorem [Frequency shifting]
Find the Z‒transform of the
following
(1) ann
(2) an/n!
(3) an/n
(4) an sin nθ
(5) an cos nθ
(6) an rn cos
nθ
(7) (n ‒ 1) an‒1
(8) an cos n π
(9) ann3
(10) a‒nn2
(11) 2n n2
(12) 2n sinh 3n
(13) an cosh an
(14) an sin nπ/2
Transforms and its Applications: UNIT 2: Z Transform : Tag: Engineering mathematics, Maths : - Z Transform: First Shifting theorem (Frequency shifting)
Transforms and its Applications: UNIT 2: Z Transform
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