[complex numbers application: transfer functions] you will deal with many "transfer functions" in your career as an electrical and computer engineer. the transfer function tells how the input and output are related for a given system. here is an example from the first midterm in ece 310, with some extra scaffolding for you, of course. suppose that i have an input signal of the form x(t) = a1e s1t + a2e s2t + . . + an e sn t . (note that the si will be complex! ) input to a system with transfer function h(s). then, the output of the system is given by y(t) = a1h(s1)e s1t + a2h(s2)e s2t + . . + an h(sn )e sn t . consider a system with transfer function h(s) = s 2 + 1 1.5s and voltage input v1(t) = 4 cos(2t). we will find the output voltage v2(t) in three steps.
(a) write v1(t) in the form v1(t) = a1e s1t + a2e s2t + . . + an e sn t (i. e. write the cosine as a sum of complex exponentials.)
(b) use y(t) = a1h(s1)e s1t +a2h(s2)e s2t +. .+an h(sn )e sn t , with the specific h(s) above, to write v2(t) as a sum of complex exponentials.
(c) covert v2(t) back to be in the form of a cosine.