Desgining butterworth filter of Nth order

I want to design a digital butterworth lowpass filter of nth order, with only freedom of choice to user being order of the filter and the cut off frequency, i already have a 1st order low pass.


This is a very basic lowpass PT1 filter, i take the state space matrix, descrtize it and apply it to my signal. now i want to extend my library to butterworth. I am trying to use as many minimal matlab commands as possible. So i thought it's better to derive in hand before implementing it. i wanted to know how to deal with damping ratio as the order is progressed.

When i was searching for answer, i came across wiki of butter worth filter:


I can just hard code this, but have they considered damping ratio and how do i covert this to state space.

Any help would be greatfull

Can you please explain the meaning of your "code". I don't see it related to known digital butterworth implementations.

That has nothing to do with digital butterworth filter, sorry for the confusion. it was just an example of how the output of the filter should be. It was a lowpass PT1 filter.

Butterworth is an IIR filter, the PT1 response to a step should be an exponential function. In case you are intending an FIR butterworth approximation you should mention this.