Practice Problems (KEY)#
Problem 1.#
Given the following system, choose the best filter and cut-off frequency.
Answer: LPF, \(f_{\text{c/o}} = 5\ \text{kHz}\)
Problem 2.#
T/F These two systems perform the same function.
Answer: True
Problem 3.#
Given that
and the Band Reject Filter below, what will \(v_{\text{out}}(t)\) be?
Answer: $$ v(t) = 3
4\cos(360^\circ \cdot 6k,t)\ \text{mV} $$
Problem 4.#
Plot the output of the following filters given that
a. LPF → \(f_{\text{c/o}} = 5\ \text{kHz}\)
b. HPF → \(f_{\text{c/o}} = 6\ \text{kHz}\)
c. BPF → \(f_{\text{c/o,1}} = 3\ \text{kHz}\) and \(f_{\text{c/o,2}} = 9\ \text{kHz}\)
d. BRF → \(f_{\text{c/o,1}} = 3\ \text{kHz}\) and \(f_{\text{c/o,2}} = 6\ \text{kHz}\)
Problem 5.#
Graph the following signal in the frequency domain:
Problem 6.#
The signal given in Practice Problem 5 above is input to each of the following filters. What is the output of each filter? Provide the frequency domain plot and the equation.
a.#
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$\(v(t) = 6 + 4\cos(360^\circ \cdot 1k\,t) + 8\cos(360^\circ \cdot 2k\,t)\ \text{mV}\)$ |
b.#
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$\(v(t) = 5\cos(360^\circ \cdot 4k\,t) + 2\cos(360^\circ \cdot 7k\,t)\ \text{mV}\)$ |
c.#
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$\(v(t) = 8\cos(360^\circ \cdot 2k\,t) + 5\cos(360^\circ \cdot 4k\,t)\ \text{mV}\)$ |
Problem 7.#
What is the bandwidth for each of the output signals in Practice Problem 6?
a.
b.
c.
Problem 8.#
You just recorded your voice using a voice recorder in a room full of equipment. The equipment emits a loud \(60\ \text{Hz}\) hum. You decide you want to eliminate the hum from your recording. Your voice ranges from \(300\) to \(3400\ \text{Hz}\). Design a filter to eliminate the hum.
Option 1: Put in a HPF with \(f_{\text{c/o}} = 150\ \text{Hz}\) (any frequency between \(60\ \text{Hz}\) and \(300\ \text{Hz}\) would work)
Option 2: Put in a BPF with \(f_{\text{c/o,1}} = 150\ \text{Hz}\) and \(f_{\text{c/o,2}} = 3500\ \text{Hz}\)