Hello,
I need to calculate the maximum value of the derivative of the response of a linear system when a specific input is applied. I am interested in getting this information during the transient response phase.
My input signale is a sequence of gaussian shapes equally shaped and separated that start at t>0.
My idea to calculate this is:
Create a Fourier series of input signal (time domain):
Q = 5*10^7*1.602*10^-19;
sigmat = (172/4)*10^-9;
Trev = 629*10^-9;
sigmaAux = sigmat*2*Pi/Trev;
input = FourierSeries[Q/(Sqrt[2*Pi]*sigmaAux)*Exp[-t^2/(2*sigmaAux^2)],
t, 10];
input[t_] = input;
input[t_] = input[t - Pi];
input[t_] = input[t*(2*Pi/Trev)];
Plot[input[t], {t, -1*10^-6, 1*10^-6}]
Compute Laplace transform of input signal, multiply it by transfer function of system and compute inverse transform of result:
transient[t_] :=
InverseLaplaceTransform[
LaplaceTransform[input[t], t, s]*2*Pi*10^5/(s + 2*Pi*10^5), s, t];
Plot[transient[t], {t, 0, 1*10^-5}, Mesh -> All]
After this I could compute derivative of signal. But the time response of the system is not right. I should be getting an output signal with "oscillations" around an increasing mean value, but I'm not getting this. The output
I've tried different things, like increasing the series order but I get the same behaviour
Any idea why this is not working?
Many thanks in advance