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<math>y(t) = \int^{\infty}_{-\infty} h(t) * x(t) dt\,</math> where <math>x(t) = 1+\sin \omega_0 t + \cos(2\omega_0 t+ \frac{\pi}{4})</math> | <math>y(t) = \int^{\infty}_{-\infty} h(t) * x(t) dt\,</math> where <math>x(t) = 1+\sin \omega_0 t + \cos(2\omega_0 t+ \frac{\pi}{4})</math> | ||
| + | |||
| + | <math>y(t) = \int^{\infty}_{-\infty} K \delta(t) * (1+\sin \omega_0 t + \cos(2\omega_0 t+ \frac{\pi}{4}))</math> | ||
Revision as of 12:12, 25 September 2008
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})) $
