Question

Suppose an output signal is composed of the product of two other signals $v_{out} = v_1(t)v_2(t)$, where: $v_1(t) = 5 + 2 \cos(2\pi 200t)$ $v_2(t) = 2 \cos(2\pi 1000t)$ Consider the power spectrum of $v_{out}(t)$. Determine the frequencies where the signal power is non-zero. Select one: a. 0 and 1000 Hz b. 200 and 1000 Hz c. 0, 200 and 1000 Hz d. 800, 1000 and 1200 Hz

          Suppose an output signal is composed of the product of two other signals $v_{out} = v_1(t)v_2(t)$, where: 
$v_1(t) = 5 + 2 \cos(2\pi 200t)$
$v_2(t) = 2 \cos(2\pi 1000t)$
Consider the power spectrum of $v_{out}(t)$. Determine the frequencies where the signal power is non-zero.
Select one:
a. 0 and 1000 Hz
b. 200 and 1000 Hz
c. 0, 200 and 1000 Hz
d. 800, 1000 and 1200 Hz

Suppose an output signal is composed of the product of two other signals vout = v1(t)v2(t), where:
v1(t) = 5 + 2 cos(2π 200t)
v2(t) = 2 cos(2π 1000t)
Consider the power spectrum of vout(t). Determine the frequencies where the signal power is non-zero.
Select one:
a. 0 and 1000 Hz
b. 200 and 1000 Hz
c. 0, 200 and 1000 Hz
d. 800, 1000 and 1200 Hz

Added by Amanda H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Arpit Gupta

09/20/2021

Step 1

Then \begin{align*} \label{eq:1} v_{out}(t) &= (5 + 2\cos(2\pi200t))(2\cos(2\pi1000t)) \\ &= 10\cos(2\pi1000t) + 4\cos(2\pi200t)\cos(2\pi1000t)\end{align*} Using the trigonometric identity $\cos A \cos B = \frac{1}{2}[\cos(A+B) + \cos(A-B)]$, we Show more…

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Suppose an output signal is composed of the product of two other signals $v_{out} = v_1(t)v_2(t)$, where: $v_1(t) = 5 + 2\cos(2\pi200t)$ $v_2(t) = 2\cos(2\pi1000t)$ Consider the power spectrum of $v_{out}(t)$. Determine the frequencies where the signal power is non-zero. Select one: a. 0 and 1000 Hz b. 200 and 1000 Hz c. 0, 200 and 1000 Hz d. 800, 1000 and 1200 Hz