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

 

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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: G(s) Input signal where K and a are real numbers. Recall that a signal is filtered as shown here, in block diagram form: K sta G(s) Output signal 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. Design a filter for one of the signals shown on the pages that follow. If the last digit in your uOttawa student ID number is in the set (3, 4, 5, 6, 7), then use the signal shown on page 6. Otherwise, the last digit of your ID number must be in the set {0, 1, 2, 8, 9), and you should use the signal shown on page 7. (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. (d) Calculate the amount by which the amplitude of the high-frequency part will change. IN Input signal (V) O Input signal (V) -1 -2 0 0.4 0.2 -0.2 2 0 4 Here is a zoomed-in view of the first 0.1 seconds: 0.6 6 Signal for {3, 4, 5, 6, 7} www. 8 10 Time (s) 12 0.01 0.02 0.03 0.04 0.05 0.06 Time (s) 14 0.07 16 0.08 18 20 0.09 0.1 Input signal (V) 3 2 1 AUAUA v 6 8 10 Time (s) -3 0 0.2 Here is a zoomed-in view of the first 0.1 seconds: 0.3 0.1 0 -0.1 2 0 Signal for {0, 1, 2, 8,9} 4 0.01 0.02 0.03 0.04 12 14 16 18 20 0.05 0.06 0.07 0.08 0.09 0.1 Time (s) 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: G(s) Input signal where K and a are real numbers. Recall that a signal is filtered as shown here, in block diagram form: K sta G(s) Output signal 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. Design a filter for one of the signals shown on the pages that follow. If the last digit in your uOttawa student ID number is in the set (3, 4, 5, 6, 7), then use the signal shown on page 6. Otherwise, the last digit of your ID number must be in the set {0, 1, 2, 8, 9), and you should use the signal shown on page 7. (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. (d) Calculate the amount by which the amplitude of the high-frequency part will change. IN Input signal (V) O Input signal (V) -1 -2 0 0.4 0.2 -0.2 2 0 4 Here is a zoomed-in view of the first 0.1 seconds: 0.6 6 Signal for {3, 4, 5, 6, 7} www. 8 10 Time (s) 12 0.01 0.02 0.03 0.04 0.05 0.06 Time (s) 14 0.07 16 0.08 18 20 0.09 0.1 Input signal (V) 3 2 1 AUAUA v 6 8 10 Time (s) -3 0 0.2 Here is a zoomed-in view of the first 0.1 seconds: 0.3 0.1 0 -0.1 2 0 Signal for {0, 1, 2, 8,9} 4 0.01 0.02 0.03 0.04 12 14 16 18 20 0.05 0.06 0.07 0.08 0.09 0.1 Time (s)