• Electrical Engineering Archive: Questions from 2024-11-24

    5.48 Find the Fourier transform of the following signals with A = 2, ω0 = 5 rad/s, α = 0.5 s−1, and ϕ0 = π/5. (a) f(t) = Acos⁡(ω0t − ϕ0), −∞ < t < ∞ (b) g(t) = e−αtcos⁡(ω0t)u(t)
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    5.52 Let the Fourier transform of f(t) be F(ω) = A (B+jω) Determine the transforms of the following signals (using A = 5 and B = 2): (a) f(3t−2) (b) tf(t) (c) df(t)/dt
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    6.4 For the circuit shown in Fig. P6.4, determine (a) the transfer function H = Vo/Vi, and (b) the frequency ωo at which H is purely real. Figure P6.4: Circuit for Problem 6.4.
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    6.10 A series RLC bandpass filter has half-power frequencies at 1 kHz and 10 kHz. If the input impedance at resonance is 6 Ω, what are the values of R, L, and C?
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    6.70 If x(t) is bandlimited to 5 kHz, what is the Nyquist sampling rate for y(t) = x2(t)?
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    7.10 Compute the following convolutions: (a) {3, 4, 5}∗{6, 7, 8} (b) {1, 2, −3}∗u[n] (c) {3, 4, 5}∗(u[n] − u[n−3]) (d) {1, 2, 4}∗2δ[n−2]
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