Introductory Circuit Analysis (13th Edition)
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ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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![Given a continuous time signal \( x(t) \). Sample the signal with a sampling rate of \( F_s = 100 \) samples/s.
\[ x(t) = \cos(2\pi 40t) \]
- What is the frequency of the cosine in Hz?
- What is the frequency of the cosine in rad/s?
- What is the frequency of the sampled cosine in normalized rad/s?
- What is the frequency of the sampled cosine in normalized Hz?
- Using \( N = 50 \), what is the DFT of the sampled signal? What are the indexes where the DFT is non-zero?
- In MATLAB, generate the sampled signal and plot the magnitude of the DFT with index \( k \) on the x-axis.
- In MATLAB, plot the magnitude of the DFT with Hz on the x-axis.](https://content.bartleby.com/qna-images/question/4bdca33e-fe41-4c4f-b2f7-f887541be3fa/9232daf9-730f-4e80-962c-f15b81dfce2b/rxjhbko_processed.png)
Transcribed Image Text:Given a continuous time signal \( x(t) \). Sample the signal with a sampling rate of \( F_s = 100 \) samples/s.
\[ x(t) = \cos(2\pi 40t) \]
- What is the frequency of the cosine in Hz?
- What is the frequency of the cosine in rad/s?
- What is the frequency of the sampled cosine in normalized rad/s?
- What is the frequency of the sampled cosine in normalized Hz?
- Using \( N = 50 \), what is the DFT of the sampled signal? What are the indexes where the DFT is non-zero?
- In MATLAB, generate the sampled signal and plot the magnitude of the DFT with index \( k \) on the x-axis.
- In MATLAB, plot the magnitude of the DFT with Hz on the x-axis.
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