An "input-output" system is excited by an input signal e(t) and provides an
output signal s(t), both zero for t < 0. Let E and S be the transforms of
Laplace of the e and s functions. The system is modeled by the transfer function
H of the system that verifies: S(p) = H(p) × E(p). A physical modelling of the
The system gives the following transfer function:
H(p) = p/(2p^2+2P+1)
In addition, the system is excited with a "slot" :e(t) = U(t) - U(t - π).
a) Determine the expression of the function e and its Laplace transform E.
b) Check that: 2p^2+2p+1=2[(p+(1/2))^2+(1/4)]
(c) Calculate S and deduce the expression of s.
output signal s(t), both zero for t < 0. Let E and S be the transforms of
Laplace of the e and s functions. The system is modeled by the transfer function
H of the system that verifies: S(p) = H(p) × E(p). A physical modelling of the
The system gives the following transfer function:
H(p) = p/(2p^2+2P+1)
In addition, the system is excited with a "slot" :e(t) = U(t) - U(t - π).
a) Determine the expression of the function e and its Laplace transform E.
b) Check that: 2p^2+2p+1=2[(p+(1/2))^2+(1/4)]
(c) Calculate S and deduce the expression of s.