Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
x(t) = Σ k= ∞ akej wok The kth term in the series is called the kth harmonic. Determine which harmonics (positive and negative) are present. In other words, for the Fourier series coefficients, ak, determine which coefficients are nonzero. List the indices of the nonzero Fourier series coefficients and their values in a table. chirn signal is one that sweens in frequency from

x(t) = Σ k= ∞ akej wok The kth term in the series is called the kth harmonic. Determine which harmonics (positive and negative) are present. In other words, for the Fourier series coefficients, ak, determine which coefficients are nonzero. List the indices of the nonzero Fourier series coefficients and their values in a table. chirn signal is one that sweens in frequency from

Introductory Circuit Analysis (13th Edition)
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...
See similar textbooks
icon
Related questions
Question

Please assist with practice question P-3.20 letter d with details on how to do it. 

**Fourier Series Representation of Periodic Signals** A periodic signal of this type can be represented as a Fourier series of the form: \[ x(t) = \sum_{k=-\infty}^{\infty} a_k e^{j\omega_0 kt} \] The \( k^{\text{th}} \) term in the series is called the \( k^{\text{th}} \) harmonic. Determine which harmonics (positive and negative) are present. In other words, for the Fourier series coefficients, \( a_k \), determine which coefficients are nonzero. List the indices of the nonzero Fourier series coefficients and their values in a table.
Transcribed Image Text:**Fourier Series Representation of Periodic Signals** A periodic signal of this type can be represented as a Fourier series of the form: \[ x(t) = \sum_{k=-\infty}^{\infty} a_k e^{j\omega_0 kt} \] The \( k^{\text{th}} \) term in the series is called the \( k^{\text{th}} \) harmonic. Determine which harmonics (positive and negative) are present. In other words, for the Fourier series coefficients, \( a_k \), determine which coefficients are nonzero. List the indices of the nonzero Fourier series coefficients and their values in a table.
### Problem P-3.20 A real signal \( x(t) \) has the two-sided spectrum shown in Figure P-3.20. The frequency axis has units of rad/s. #### Graph Explanation: The graph in Figure P-3.20 shows a two-sided spectrum with the frequency axis labeled in rad/s. The specific points and their values along the frequency axis (\(\omega\)) are: - At \(\omega = -90\): - Amplitude = \(0.4e^{-j2}\) - At \(\omega = -40\): - Amplitude = \(0.6e^{j1.4}\) - At \(\omega = 0\): - Amplitude = \(0.5\) - At \(\omega = 40\): - Amplitude = \(0.6e^{-j1.4}\) - At \(\omega = 90\): - Amplitude = \(0.4e^{j2}\) #### Questions (a) Determine the fundamental frequency \(\omega_0\) of this signal. (b) Determine the fundamental period \(T_0\) of \(x(t)\), which is the shortest possible period. (c) Determine the DC value of this signal.
Transcribed Image Text:### Problem P-3.20 A real signal \( x(t) \) has the two-sided spectrum shown in Figure P-3.20. The frequency axis has units of rad/s. #### Graph Explanation: The graph in Figure P-3.20 shows a two-sided spectrum with the frequency axis labeled in rad/s. The specific points and their values along the frequency axis (\(\omega\)) are: - At \(\omega = -90\): - Amplitude = \(0.4e^{-j2}\) - At \(\omega = -40\): - Amplitude = \(0.6e^{j1.4}\) - At \(\omega = 0\): - Amplitude = \(0.5\) - At \(\omega = 40\): - Amplitude = \(0.6e^{-j1.4}\) - At \(\omega = 90\): - Amplitude = \(0.4e^{j2}\) #### Questions (a) Determine the fundamental frequency \(\omega_0\) of this signal. (b) Determine the fundamental period \(T_0\) of \(x(t)\), which is the shortest possible period. (c) Determine the DC value of this signal.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS