Transforms and its Applications: UNIT 2: Z Transform

Z Transform: Initial value theorem and final value theorem

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Z Transform: Example Important Solved Problems with formula, steps, derivation and answer based on Z Transform - Initial value theorem and final value theorem.

Initial value theorem and final value theorem.

 

1. Initial value theorem

If Z [f(n)] = F(z), then f(0) = limz→∞ F(z)

Proof :


 

2. Final value theorem.

If Z{f(n)} = F(z), then lim n→∞ [f(n)] = limz→1 (z − 1) F(z)

Proof:


 

Problems based on initial value theorem and final value theorem




Transforms and its Applications: UNIT 2: Z Transform : Tag: Engineering mathematics, Maths : - Z Transform: Initial value theorem and final value theorem

Home | Department: EEE Department | Ist Year | Subject: Transforms and its Applications |
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Transforms and its Applications: UNIT 2: Z Transform


Applications of Z transform

Z - transform of standard functions

Z Transform Linearity property

Z Transform: Differentiation in the Z-Domain

Z Transform: First Shifting theorem (Frequency shifting)

Z Transform: Second shifting theorem (Time Shifting)

Z Transform: Unit impulse sequence and unit step sequence

Z Transform: Initial value theorem and final value theorem

Z Transform: Differentiation

Inverse Z Transform: Partial Fractions Methods

Inverse Z Transform: Inverse integral method (Cauchy's residue theorem)

Z Transform: Convolution Theorem

Z Transform: Formation of difference equations

Application: Solution of difference equations using Z transform

Z Transform: Exercise Problems

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