
Example 8.10
An input signal u(t) ¼sin vt, t 0 is sampled every T ¼0.1 s, and the resulting discrete-time signal
u
n
, n ¼0, 1, 2,...is input to an extrapolator governed by Equation 8.358.
(a) Graph the continuous-time signal u(t), discrete-time signal u
n
, and the extrapolator output
^
u
nþ1
, n ¼ 0, 1, 2, 3, ... for the following cases:
(i) vT ¼0.1 rad
(ii) vT ¼0.25 rad
(iii) vT ¼0.5 rad
(iv) vT ¼1 rad
(b) An improved Euler integrator with step size T ¼0.1 s is used to simulate the response of the
first-order system in Equation 8.339 to the sinusoidal input u(t) ¼sin vt, t 0. In order to
simulate the real-time response, the input is extrapolated as shown ...