how to differentiation code,?
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i want to wirte x*(1+s) into matlab function block in c code
wher x is input signal and s - is s laplace i.e. use for differentation in matlab
please help
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Answers (1)
Benjamin Thompson
on 1 Feb 2022
Edited: Benjamin Thompson
on 1 Feb 2022
If you have x as sampled signal in time, differentiation is easy: (x(t2) - x(t1)) / (t2 - t1)
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Benjamin Thompson
on 2 Feb 2022
LaPlace notation is used for convenience to work with differential equations algebraically, for analysis or simplification, solving for parameters, etc. If you want a time based numerical solution to a differential or difference equation, you must convert to the time representation. In the case of differentiation that is fairly trivial.
Walter Roberson
on 3 Feb 2022
For any given numeric k, you can construct the numeric tf(), and use c2d() to find the equivalent discrete transfer function, the coefficients of which can be used to filter()
I just spent a while tracing through c2d, as I expected that there might be a relatively simple conversion for this case of 1/(k*s+1) .
Unfortunately, the internal construction of ss form involves a 2^round(log2(sqrt(1/k))) to construct a scaling factor, which makes the conversion a bit more complicated.
I kept looking through anyhow, thinking that at least in theory that might not be necessary, that you might be able to proceed with state space a=-1/k, b = 1, c = 1/k, d = 0, e = [] .
Sadly, inside the routine to discretize from zero order hold, there is a call to the undocumented mex routine matscale
I see hints that maybe you could use
Phi = exp(-Ts/k)
Gamma = k - k*exp(-Ts/k)
and
x[n+1] = Phi * x[n] + Gamma * u[n]
but I am not sure how that would translate into filter() or conv()
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