The frequency-domain input-output relationship is portrayed in Fig. 17.17.
Equation (17.55) shows that if we know the transfer function and the input,
we can readily find the output. The relationship in Eq. (17.54) is
the principal reason for using the Fourier transform in circuit analysis.
Notice that H(ω) is identical to H(s) with s = jω. Also, if the input
is an impulse function [i.e., x(t) = δ(t)], then X(ω) = 1, so that the
response is