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Ques. 7: Find the exponential Fourier series representation of the following signals: (a) = y(t) = 4cos (2w,t) (b) y(t) = cos²(t)

Ques. 7: Find the exponential Fourier series representation of the following signals: (a) = y(t) = 4cos (2w,t) (b) y(t) = cos²(t)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Question 7: Find the Exponential Fourier Series Representation **Problem Statement:** Determine the exponential Fourier series representation for the following signals: **(a)** \[ y(t) = 4 \cos(2\omega_0 t) \] **(b)** \[ y(t) = \cos^2(t) \] Since there are no additional graphs or diagrams associated with this question, explanations for the signals should focus on deriving their respective Fourier series representations. **Solution Strategy:** _For part (a)_: Express the cosine function in its exponential form using Euler's formula: \[ \cos(\theta) = \frac{e^{j\theta} + e^{-j\theta}}{2} \] _For part (b)_: Use trigonometric identities and Euler's formula to express the square of a cosine function in terms of exponential functions.
Transcribed Image Text:### Question 7: Find the Exponential Fourier Series Representation **Problem Statement:** Determine the exponential Fourier series representation for the following signals: **(a)** \[ y(t) = 4 \cos(2\omega_0 t) \] **(b)** \[ y(t) = \cos^2(t) \] Since there are no additional graphs or diagrams associated with this question, explanations for the signals should focus on deriving their respective Fourier series representations. **Solution Strategy:** _For part (a)_: Express the cosine function in its exponential form using Euler's formula: \[ \cos(\theta) = \frac{e^{j\theta} + e^{-j\theta}}{2} \] _For part (b)_: Use trigonometric identities and Euler's formula to express the square of a cosine function in terms of exponential functions.
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