Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(a) Determine the fundamental frequency wo of this signal. (b) Determine the fundamental period To of x (t), which is the shortest possible period. (c) Determine the DC value of this signal.

(a) Determine the fundamental frequency wo of this signal. (b) Determine the fundamental period To of x (t), which is the shortest possible period. (c) Determine the DC value of this signal.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

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

**Problem P-3.20: Frequency Analysis of a Real Signal** A real signal \( x(t) \) has the two-sided spectrum shown in Fig. P-3.20. The frequency axis has units of rad/s. **Figure P-3.20: Two-sided Spectrum** The graph demonstrates the two-sided spectrum of the real signal \( x(t) \). The horizontal axis represents the angular frequency (\( \omega \)) in rad/s, and the vertical axis denotes the amplitude of the signal components. - At \(\omega = -90 \, \text{rad/s}\), the amplitude is \( 0.4e^{-j2} \). - At \(\omega = -40 \, \text{rad/s}\), the amplitude is \( 0.6e^{j1.4} \). - At \(\omega = 0 \, \text{rad/s}\), the amplitude is \( 0.5 \). - At \(\omega = 40 \, \text{rad/s}\), the amplitude is \( 0.6e^{-j1.4} \). - At \(\omega = 90 \, \text{rad/s}\), the amplitude is \( 0.4e^{j2} \). ### 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: Frequency Analysis of a Real Signal** A real signal \( x(t) \) has the two-sided spectrum shown in Fig. P-3.20. The frequency axis has units of rad/s. **Figure P-3.20: Two-sided Spectrum** The graph demonstrates the two-sided spectrum of the real signal \( x(t) \). The horizontal axis represents the angular frequency (\( \omega \)) in rad/s, and the vertical axis denotes the amplitude of the signal components. - At \(\omega = -90 \, \text{rad/s}\), the amplitude is \( 0.4e^{-j2} \). - At \(\omega = -40 \, \text{rad/s}\), the amplitude is \( 0.6e^{j1.4} \). - At \(\omega = 0 \, \text{rad/s}\), the amplitude is \( 0.5 \). - At \(\omega = 40 \, \text{rad/s}\), the amplitude is \( 0.6e^{-j1.4} \). - At \(\omega = 90 \, \text{rad/s}\), the amplitude is \( 0.4e^{j2} \). ### 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.**
**Chapter 3: Spectrum Analysis** ### Periodic Signal Representation using Fourier Series A periodic signal of this type can be represented as a Fourier series of the form: \[ x(t) = \sum_{k=-\infty}^{\infty} a_k e^{j\omega_0kt} \] The \( k^{th} \) term in the series is called the \( k^{th} \) 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:**Chapter 3: Spectrum Analysis** ### Periodic Signal Representation using Fourier Series A periodic signal of this type can be represented as a Fourier series of the form: \[ x(t) = \sum_{k=-\infty}^{\infty} a_k e^{j\omega_0kt} \] The \( k^{th} \) term in the series is called the \( k^{th} \) 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.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS