Question: The following problems are about the steady state response of LTI systems due to periodic signals. (a) The transfer function of a LTI system is

The following problems are about the steady state response of LTI systems due to periodic signals.

(a) The transfer function of a LTI system is

Y (s) s+ 1 H(s) X(s) s2 + 3s + 2

If the input to this system is x(t) = 1 + cos(t + π/4) what is the output y(t) in the steady state.

(b) The transfer function of a LTI system is given by

Y (s) H(s) X(s) s* + 3s +2

and its input is x(t) = 4u(t).

i. Use the eigenfunction property of LTI systems to find the steady-state response y(t) of this system.

ii. Verify your result above by means of the Laplace transform.

Y (s) s+ 1 H(s) X(s) s2 + 3s + 2 Y (s) H(s) X(s) s* + 3s +2

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