An LTI system with frequency response $H(j\omega) = \frac{j(\omega - \omega_0)}{\omega_0 + j(\omega - \omega_0)}$ is excited with the input signal $x(t) = cos(\omega_0t) + cos(2\omega_0t)$. Determine the output $y(t)$ of the system.
Added by Mar M.
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Step 1
First, let's find the Fourier transform of the input signal x(t). The Fourier transform of cos(wot) is a Dirac delta function centered at wo, and the Fourier transform of cos(2wot) is a Dirac delta function centered at 2wo. Therefore, the Fourier transform of x(t) Show more…
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