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2. Consider the following RC network whose input voltage is the x(t) signal and its output voltage is the voltage of the capacitor y(t). Think about it as an LTI system with the input signal x(t) that produces output signal y(t). R x(t) W C y(t) It can be shown that the Fourier transform of the impulse response of this system is H(jw) : is the resistance of the resistor and C is the capacity of the capacitor. = 1 1+RCjw 1+ RTC jw where R (a) Let R = 30 and C = 10-4F. Compute the response of this system to the input z(t) = cos(wot) for some Wo > 0. ωο (b) Using MATLAB, plot the signal x(t) = cos(3t) + cos(105t) for t = [0,π). tЄ (c) Compute the output y(t) of the system for the above input x(t). (d) Plot y(t). What does this system do?

2. Consider the following RC network whose input voltage is the x(t) signal and its output voltage is the voltage of the capacitor y(t). Think about it as an LTI system with the input signal x(t) that produces output signal y(t). R x(t) W C y(t) It can be shown that the Fourier transform of the impulse response of this system is H(jw) : is the resistance of the resistor and C is the capacity of the capacitor. = 1 1+RCjw 1+ RTC jw where R (a) Let R = 30 and C = 10-4F. Compute the response of this system to the input z(t) = cos(wot) for some Wo > 0. ωο (b) Using MATLAB, plot the signal x(t) = cos(3t) + cos(105t) for t = [0,π). tЄ (c) Compute the output y(t) of the system for the above input x(t). (d) Plot y(t). What does this system do?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2. Consider the following RC network whose input voltage is the x(t) signal and its output voltage is the voltage of the capacitor y(t). Think about it as an LTI system with the input signal x(t) that produces output signal y(t). R x(t) W C y(t) It can be shown that the Fourier transform of the impulse response of this system is H(jw) : is the resistance of the resistor and C is the capacity of the capacitor. = 1 1+RCjw 1+ RTC jw where R (a) Let R = 30 and C = 10-4F. Compute the response of this system to the input z(t) = cos(wot) for some Wo > 0. ωο (b) Using MATLAB, plot the signal x(t) = cos(3t) + cos(105t) for t = [0,π). tЄ (c) Compute the output y(t) of the system for the above input x(t). (d) Plot y(t). What does this system do?
Transcribed Image Text:2. Consider the following RC network whose input voltage is the x(t) signal and its output voltage is the voltage of the capacitor y(t). Think about it as an LTI system with the input signal x(t) that produces output signal y(t). R x(t) W C y(t) It can be shown that the Fourier transform of the impulse response of this system is H(jw) : is the resistance of the resistor and C is the capacity of the capacitor. = 1 1+RCjw 1+ RTC jw where R (a) Let R = 30 and C = 10-4F. Compute the response of this system to the input z(t) = cos(wot) for some Wo > 0. ωο (b) Using MATLAB, plot the signal x(t) = cos(3t) + cos(105t) for t = [0,π). tЄ (c) Compute the output y(t) of the system for the above input x(t). (d) Plot y(t). What does this system do?
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