Introductory Circuit Analysis (13th Edition)
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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.](https://content.bartleby.com/qna-images/question/091efdc9-e15b-4ccc-8207-a2051acfb2c9/9056482f-9814-4af6-a9d1-27d2759c224a/rye93y_processed.png)
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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