Problem No.3 Based on Inverse Z-transform | Ekeeda.com

Inverse Z Transform:
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, golden rule) is a basic method for pseudo-random number sampling, i.e. for generating sample numbers at random from any probability distribution given its.
• Formal inverse z-transform is based on a Cauchy integral
• Less formal ways sufficient most of the time
1. Inspection method
2. Partial fraction expansion
3. Power series expansion

Inverse Z-Transform by Partial Fraction Expansion:
• First term exist only if M Greater than N.
– Br is obtained by long division
• Second term represents all first order poles
• Third term represents an order s pole
– There will be a similar term for every high-order pole
• Each term can be inverse transformed by inspection

Inverse Z-Transform by Power Series Expansion:
• Z-transforms of this form can generally be inversed easily
• Especially useful for finite-length series

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