Question

Q1) Let the input to the system shown in Fig Q1, to be $x(t) = 4 + 12 \cos^2(\pi f_0 t) + 8 \sin(2\pi f_0 t) + 10 \sin(4\pi f_0 t)$, and the transfer function $\begin{cases} 1/5 & -1.5f_0 < f < 1.5f_0 \\ 0 & \text{otherwise} \end{cases}$ $H(f) =$ x(t) y(t) h(t) Fig Q1 a) Find and Plot the frequency spectra (amplitude & phase) for the input and the output. b) Find and plot the power spectral density for the input $G_i(f)$, and the output $G_o(f)$. c) Find the normalized input power $S_i$, and the normalized output power $S_o$. d) Find the power gain in dB.

          Q1) Let the input to the system shown in Fig Q1, to be
$x(t) = 4 + 12 \cos^2(\pi f_0 t) + 8 \sin(2\pi f_0 t) + 10 \sin(4\pi f_0 t)$, and the transfer function
$\begin{cases} 1/5 & -1.5f_0 < f < 1.5f_0 \\ 0 & \text{otherwise} \end{cases}$
$H(f) =$
x(t)
y(t)
h(t)
Fig Q1
a) Find and Plot the frequency spectra (amplitude & phase) for the input and the
output.
b) Find and plot the power spectral density for the input $G_i(f)$, and the output
$G_o(f)$.
c) Find the normalized input power $S_i$, and the normalized output power $S_o$.
d) Find the power gain in dB.

Q1) Let the input to the system shown in Fig Q1, to be
x(t) = 4 + 12 cos^2(π f0 t) + 8 sin(2π f0 t) + 10 sin(4π f0 t), and the transfer function
1/5 -1.5f0 < f < 1.5f0
0 otherwise
H(f) =
x(t)
y(t)
h(t)
Fig Q1
a) Find and Plot the frequency spectra (amplitude phase) for the input and the
output.
b) Find and plot the power spectral density for the input Gi(f), and the output
Go(f).
c) Find the normalized input power Si, and the normalized output power So.
d) Find the power gain in dB.

Added by Jose Manuel D.

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