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Consider the square wave shown in the picture below (with a frequency of = 1 rad/s). atos 2π Using Fourier analysis, this square wave can be decomposed into the following set of harmonics: Phase (rad.) 0 -0.2 If this signal is input into an ideal low pass filter with cutoff frequency of 5 rad/s (i.e. a perfect filter with gain = 1 for <5 rad/s and gain=0 for ≥ 5 rad/s) and a phase shift given below, then write the output signal. Explain the reasoning behind your logic. Some potentially useful numbers are provided next to the plot below. -0.4 -0.6 -0.8 _y(t) = 1⁄2 + -1+ -1.2- -1.4 -1.6 102 2 (2k-1) 10-1 = sin((2k – 1)t) = 10⁰ Frequency (rad s¹) 1 2 +=sin(t) + sin(3t) +... 3T 10¹ p(0) = 0 rad. p(0.1) = -0.1 rad. p(1) = -0.79 rad. (3) = -1.25 rad. (5) = -1.37 rad.

Consider the square wave shown in the picture below (with a frequency of = 1 rad/s). atos 2π Using Fourier analysis, this square wave can be decomposed into the following set of harmonics: Phase (rad.) 0 -0.2 If this signal is input into an ideal low pass filter with cutoff frequency of 5 rad/s (i.e. a perfect filter with gain = 1 for <5 rad/s and gain=0 for ≥ 5 rad/s) and a phase shift given below, then write the output signal. Explain the reasoning behind your logic. Some potentially useful numbers are provided next to the plot below. -0.4 -0.6 -0.8 _y(t) = 1⁄2 + -1+ -1.2- -1.4 -1.6 102 2 (2k-1) 10-1 = sin((2k – 1)t) = 10⁰ Frequency (rad s¹) 1 2 +=sin(t) + sin(3t) +... 3T 10¹ p(0) = 0 rad. p(0.1) = -0.1 rad. p(1) = -0.79 rad. (3) = -1.25 rad. (5) = -1.37 rad.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Consider the square wave shown in the picture below (with a frequency of = 1 rad/s). atos 2 T Using Fourier analysis, this square wave can be decomposed into the following set of harmonics: Phase (rad.) 0 -0.2 -0.4 -0.6 If this signal is input into an ideal low pass filter with cutoff frequency of 5 rad/s (i.e. a perfect filter with gain = 1 for <5 rad/s and gain=0 for ≥ 5 rad/s) and a phase shift given below, then write the output signal. Explain the reasoning behind your logic. Some potentially useful numbers are provided next to the plot below. -0.8 -1 -1.2 -1.4 -1.6 y(t) = 10-2 k=1 10-1 2 (2k-1)π 1 1 2 - sin((2k-1)t) + =sin(t) + sin(3t) +... 3π 0 10⁰ Frequency (rad s-¹) 10¹ 10² p(0) = 0 rad. p(0.1) = -0.1 rad. (1) = -0.79 rad. (3) = -1.25 rad. (5) = -1.37 rad.
Transcribed Image Text:Consider the square wave shown in the picture below (with a frequency of = 1 rad/s). atos 2 T Using Fourier analysis, this square wave can be decomposed into the following set of harmonics: Phase (rad.) 0 -0.2 -0.4 -0.6 If this signal is input into an ideal low pass filter with cutoff frequency of 5 rad/s (i.e. a perfect filter with gain = 1 for <5 rad/s and gain=0 for ≥ 5 rad/s) and a phase shift given below, then write the output signal. Explain the reasoning behind your logic. Some potentially useful numbers are provided next to the plot below. -0.8 -1 -1.2 -1.4 -1.6 y(t) = 10-2 k=1 10-1 2 (2k-1)π 1 1 2 - sin((2k-1)t) + =sin(t) + sin(3t) +... 3π 0 10⁰ Frequency (rad s-¹) 10¹ 10² p(0) = 0 rad. p(0.1) = -0.1 rad. (1) = -0.79 rad. (3) = -1.25 rad. (5) = -1.37 rad.
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