LTI System: $ y(t) = Kx(t)\, $ where K is a constant
Unit Impulse Response: $ h(t) = K \delta(t)\, $
Frequency Response:
$ y(t) = \int^{\infty}_{-\infty} h(t) * x(t) dt\, $ where $ x(t) = 1+\sin \omega_0 t + \cos(2\omega_0 t+ \frac{\pi}{4}) $
$ y(t) = \int^{\infty}_{-\infty} K \delta(t) * (1+\sin \omega_0 t + \cos(2\omega_0 t+ \frac{\pi}{4})) $
