- 1. Getting Started with UML State Machines and Event-Driven Programming
- from Practical UML Statecharts in C/C++, 2nd Edition
- Publisher: CRC Press
- Released: May 2013
The transfer function (in Z-transform) of a first order low-pass filter is TF = kz^-1/(1-(1-k)z^-1) in which 1/k is the time constant. Using a time constant of 2^n, TF = (1/2^n)/(z-(2^n-1)/2^n).
Let x(k) and y(k) be the input and the output.
y(z)/x(z) = (1/2^n)/(z-(2^n-1)/2^n) (z-(2^n-1)/2^n)y(z)=(1/2^n)x(z) y(z)=((2^n-1)/2^n)(z^-1)y(z)+(1/2^n)(z^-1)x(z)
Take the inverse Z-transform
When n = 3
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