Transforms and its Applications: UNIT 2: Z Transform
Z Transform: Unit impulse sequence and unit step sequence
Z Transform: Example Important Solved Problems with formula, steps, derivation and answer based on Z Transform -Unit impulse sequence and unit step sequence. Definition, Proof, derivation of Unit impulse sequence and unit step sequence.
Unit impulse sequence and unit step sequence
Definition: Unit impulse sequence
The
unit impulse sequence δ(n) is defined as the sequence with values
δ(n)
= 1 for n=0
δ(n)
= 0 for n ≠0
(1) Z‒Transfrom
of unit impulse sequence is 1. i.e., Z [δ (n)] = 1
Proof:
Definition: Unit step sequence
The
unit step sequence u (n) has values
u
(n) = 1 for n >0
u
(n) = 0 for n < 0
(2) Z‒transform
of unit step sequence i.e., Z (u (n)} = z / z−1
Proof:
(3) Z‒transform
of an u(n) is z / z‒a is |z|>a
Proof:
Find the Z‒transform of the following. (based on unit impulse sequence and unit step sequence)
(1) δ(n‒k)
(2) an δ(n‒k)
(3) 2n δ(n – 2)
(4) 3n δ(n − 1)
(5) u (n ‒ 1)
(6) cos nπ/2 u(n)
(0) −an u(‒n ‒ 1)
(7) (1/2)n u(n)
Transforms and its Applications: UNIT 2: Z Transform : Tag: Engineering mathematics, Maths : - Z Transform: Unit impulse sequence and unit step sequence
Transforms and its Applications: UNIT 2: Z Transform
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