Comprehensive Problems

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Comprehensive Problems

18.68 The voltage signal at the input of a filter is v(t) = 50e⁻2∣t^∣ V. What percentage of the total 1-Ω energy content lies in the frequency range of 1 < ω< 5 rad/s?

18.69 A signal with Fourier transform

$$F(\omega) = \frac{20}{4 + j\omega}$$

is passed through a filter whose cutoff frequency is 2 rad/s (i.e., 0 < ω< 2). What fraction of the energy in the input signal is contained in the output signal?

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