Donatello was assembling an electrical system and noticed high-frequency noise on two of the wires in his system. Being

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Donatello was assembling an electrical system and noticed
high-frequency noise on two of the wires in his system. Being an
expert at using Bode plots, he decided to design first-order
low-pass filters of the following form:

Donatello Was Assembling An Electrical System And Noticed High Frequency Noise On Two Of The Wires In His System Being 1 (2.43 KiB) Viewed 23 times

where 𝐾 and 𝑎 are real numbers. Recall that a signal is filtered
as shown here, in block diagram form:

Donatello Was Assembling An Electrical System And Noticed High Frequency Noise On Two Of The Wires In His System Being 2 (8.38 KiB) Viewed 23 times

Determine the values of 𝐾 and 𝑎 to satisfy the following
properties:
 The amplitude of the low-frequency part (the “useful” part)
should not change substantially.
 The amplitude of the high-frequency part (the “noise” part)
should be reduced.
(a) Find an expression for the voltage as a function of
time, making reasonable approximations based on the data provided
in the plots. The signal is comprised of a low-frequency sinusoid
and a high- frequency sinusoid.
(b) Design a filter (i.e., determine 𝐾 and 𝑎 in 𝐺(𝑠)) that
satisfies the requirements listed above.
(c) Calculate the amount by which the amplitude of the
low-frequency part will change.

Donatello Was Assembling An Electrical System And Noticed High Frequency Noise On Two Of The Wires In His System Being 3 (176.65 KiB) Viewed 23 times

G(S) K K sta
Input signal G(s) ► Output signal
N 1 Input signal (V) MW -2 0 N 4 6 8 12 14 16 18 20 10 Time (s)
Here is a zoomed-in view of the first 0.1 seconds: 0.6 0.4 Input signal (V) 0.2 0 -0.2 0 0.01 0.02 0.03 0.04 0.06 0.07 0.08 0.09 0.1 0.05 Time (s)