= (t) = - 6cos (500nt) , T = + Jsing the CTFS table of transforms and the CTFS properties, identify the CTFS harmonic function of the given perlodic signal using the representation time Tindicated. Multiple Cholce -6cos (500xt) -3 (8 (k – 5] + 8 [k + 5]) –6cos (5007t) –3 (8 [k – 5] – 8 [k + 5))
= (t) = - 6cos (500nt) , T = + Jsing the CTFS table of transforms and the CTFS properties, identify the CTFS harmonic function of the given perlodic signal using the representation time Tindicated. Multiple Cholce -6cos (500xt) -3 (8 (k – 5] + 8 [k + 5]) –6cos (5007t) –3 (8 [k – 5] – 8 [k + 5))
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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![## Problem Statement
Given the signal:
\[ x(t) = -6\cos(500\pi t), \quad T = \frac{1}{50} \]
Use the CTFS (Continuous-Time Fourier Series) table of transforms and the CTFS properties to identify the CTFS harmonic function of the given periodic signal using the representation time \( T \) indicated.
## Multiple Choice Options
1.
\[
-6\cos(500\pi t) \xleftrightarrow{\text{FS}} \frac{1}{10} \, 3 \left( \delta [k-5] + \delta [k+5] \right)
\]
2.
\[
6\cos(500\pi t) \xleftrightarrow{\text{FS}} \frac{1}{10} \, 3 \left( \delta [k-5] - \delta [k+5] \right)
\]
3.
\[
-6\cos(500\pi t) \xleftrightarrow{\text{FS}} \frac{1}{10} \, 3 \left( \delta [k-5] - \delta [k+5] \right)
\]
4.
\[
6\cos(500\pi t) \xleftrightarrow{\text{FS}} \frac{1}{10} \, 3 \left( \delta [k-5] + \delta [k+5] \right)
\]
Here, \(\delta[k]\) represents the discrete-time delta function. Choose the correct harmonic function representation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbb8af0c-abe4-42e5-b157-c6f61886cbce%2F7a9e9c98-f6e2-483d-87a6-41c42705dabf%2Fy7ptw44_processed.png&w=3840&q=75)
Transcribed Image Text:## Problem Statement
Given the signal:
\[ x(t) = -6\cos(500\pi t), \quad T = \frac{1}{50} \]
Use the CTFS (Continuous-Time Fourier Series) table of transforms and the CTFS properties to identify the CTFS harmonic function of the given periodic signal using the representation time \( T \) indicated.
## Multiple Choice Options
1.
\[
-6\cos(500\pi t) \xleftrightarrow{\text{FS}} \frac{1}{10} \, 3 \left( \delta [k-5] + \delta [k+5] \right)
\]
2.
\[
6\cos(500\pi t) \xleftrightarrow{\text{FS}} \frac{1}{10} \, 3 \left( \delta [k-5] - \delta [k+5] \right)
\]
3.
\[
-6\cos(500\pi t) \xleftrightarrow{\text{FS}} \frac{1}{10} \, 3 \left( \delta [k-5] - \delta [k+5] \right)
\]
4.
\[
6\cos(500\pi t) \xleftrightarrow{\text{FS}} \frac{1}{10} \, 3 \left( \delta [k-5] + \delta [k+5] \right)
\]
Here, \(\delta[k]\) represents the discrete-time delta function. Choose the correct harmonic function representation.
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