MATLAB: Determine the Length of One Oscillation

determine length of one oscillation

Hi everyone,
My Z-transform function is H(z) = (-3*z^2 + 4*z)/(8*z^3 -14*z^2 + 8*z -2). After plotted its response frequency, how do I determine the length of one oscillation? Any your help or hint is really appreciated!

Best Answer

That transfer function does not oscillate. It has an infinite gain over time, so if you feed in even a single non-zero value and the rest 0, it will reach an arbitrarily large output with the same sign() as the single input.
The inverse laplacian gives
(1/4)*exp(t) - (5/8)*cos((1/8)*sqrt(7)*t)*exp((3/8)*t) - (11/56)*sqrt(7)*exp((3/8)*t)*sin((1/8)*sqrt(7)*t)
and although the sin() of sqrt(7)/8 * t implies there is a layer of oscillation of period 8*2*Pi/sqrt(7), that is overwhelmed by the exp(t)/r
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