# Can't find inverse Z transform

1. May 21, 2017

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1. The problem statement, all variables and given/known data
I got the laplace transfer function H(s) = 1/(s + 2) and I'm suppose to find the inverse Z transform by first converting to H(z) by s = Ts/2*(z-1)/(z+1)
Then do inverse Z-transform using the "displacement rule" - Never heard of.

2. Relevant equations
H(s) = 1/(s + 2)
s = Ts/2*(z-1)/(z+1)

3. The attempt at a solution

I can't get any serious answer, and the partial z-inverse that I manage to find it's incredibly complicated (see image).

What is this 'displacement rule' and how do I use it here?

Last edited: May 21, 2017
2. May 21, 2017

### FactChecker

I don't have reference 17 (James G. Advanced modern engineering mathematics. Reading: Addison-Wesley; 1993.) that they refer to, but it looks like this paper ( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5240402/ ) uses it to associate the scaled/shift inside δ(γk-λtot(t)) of equation 13 with (1/γ)ztot(t)/γ in equation 15.
Conversions like that are fairly common in transformations involving the delta function.

3. May 22, 2017