_s) Express the following signal, which represents a composite EEG signal reflecting brain wave activity, in terms of a single sinusoidal function: y(t) = 3 sin(400лt +л/6)+2 cos(400лt - л/4) To do this, use the following: y₁(t) = A₁ sin(wt +0₁), y₂(t) = A₂ cos(wt + 02) and y³(t) = y₁(t) + y2(t) = A3 cos(wt + 03) where: A¸ = [A² + A² + 2A₁A₂ sin(0₁ − 0₂)]¹1/2 and 03 = tan-1 [-A₁ cos 0₁ + A₂ sin 02] A₁ sin 01 + A2 cos 02 (s) Now, confirm your answer by plotting y(t) using MATLAB. Plot y(t) over a period using a sampling Irequency of 100 kHz. Determine the amplitude and phase from the plot, and compare these with the results from part (a). You can determine the phase as follows: A cosine function with zero phase (0 = 0) reaches its maximum amplitude at t = 0. To calculate the phase, find the time (starting at t = = 0) at which the signal first reaches its maximum amplitude. Convert this time to radians and compare with the result 03 from part (a).
_s) Express the following signal, which represents a composite EEG signal reflecting brain wave activity, in terms of a single sinusoidal function: y(t) = 3 sin(400лt +л/6)+2 cos(400лt - л/4) To do this, use the following: y₁(t) = A₁ sin(wt +0₁), y₂(t) = A₂ cos(wt + 02) and y³(t) = y₁(t) + y2(t) = A3 cos(wt + 03) where: A¸ = [A² + A² + 2A₁A₂ sin(0₁ − 0₂)]¹1/2 and 03 = tan-1 [-A₁ cos 0₁ + A₂ sin 02] A₁ sin 01 + A2 cos 02 (s) Now, confirm your answer by plotting y(t) using MATLAB. Plot y(t) over a period using a sampling Irequency of 100 kHz. Determine the amplitude and phase from the plot, and compare these with the results from part (a). You can determine the phase as follows: A cosine function with zero phase (0 = 0) reaches its maximum amplitude at t = 0. To calculate the phase, find the time (starting at t = = 0) at which the signal first reaches its maximum amplitude. Convert this time to radians and compare with the result 03 from part (a).
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
![_s) Express the following signal, which represents a composite EEG signal reflecting brain wave activity,
in terms of a single sinusoidal function:
y(t) = 3 sin(400лt +л/6)+2 cos(400лt - л/4)
To do this, use the following:
y₁(t) = A₁ sin(wt +0₁), y₂(t) = A₂ cos(wt + 02) and y³(t) = y₁(t) + y2(t) = A3 cos(wt + 03)
where:
A¸ = [A² + A² + 2A₁A₂ sin(0₁ − 0₂)]¹1/2 and 03
= tan-1
[-A₁ cos 0₁ + A₂ sin 02]
A₁ sin 01 + A2 cos 02
(s) Now, confirm your answer by plotting y(t) using MATLAB. Plot y(t) over a period using a sampling
Irequency of 100 kHz. Determine the amplitude and phase from the plot, and compare these with the results
from part (a). You can determine the phase as follows: A cosine function with zero phase (0 = 0) reaches its
maximum amplitude at t = 0. To calculate the phase, find the time (starting at t = = 0) at which the signal first
reaches its maximum amplitude. Convert this time to radians and compare with the result 03 from part (a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F244d6c99-1af7-41f8-abd2-7460c0e18ea6%2F4a5ff8f4-d6c8-49f6-adf0-7859caf182fc%2Fblbva8r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:_s) Express the following signal, which represents a composite EEG signal reflecting brain wave activity,
in terms of a single sinusoidal function:
y(t) = 3 sin(400лt +л/6)+2 cos(400лt - л/4)
To do this, use the following:
y₁(t) = A₁ sin(wt +0₁), y₂(t) = A₂ cos(wt + 02) and y³(t) = y₁(t) + y2(t) = A3 cos(wt + 03)
where:
A¸ = [A² + A² + 2A₁A₂ sin(0₁ − 0₂)]¹1/2 and 03
= tan-1
[-A₁ cos 0₁ + A₂ sin 02]
A₁ sin 01 + A2 cos 02
(s) Now, confirm your answer by plotting y(t) using MATLAB. Plot y(t) over a period using a sampling
Irequency of 100 kHz. Determine the amplitude and phase from the plot, and compare these with the results
from part (a). You can determine the phase as follows: A cosine function with zero phase (0 = 0) reaches its
maximum amplitude at t = 0. To calculate the phase, find the time (starting at t = = 0) at which the signal first
reaches its maximum amplitude. Convert this time to radians and compare with the result 03 from part (a).
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