
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
![### Transcription for Educational Website
**A continuous-time signal \( x_a(t) \) has a continuous-time Fourier transform \( X_a(\Omega) = \int_{-\infty}^{\infty} x_a(t) e^{-j\Omega t} dt \) shown below:**
#### Graph Description:
- The graph is a single triangle centered at the origin.
- The x-axis is labeled \( \Omega \) (in rad/sec).
- The y-axis shows \( X_a(\Omega) \).
- The peak of the triangle is at \( \Omega = 0 \) with a maximum value of 1.
- The base of the triangle extends from \( \Omega = -100\pi \) to \( \Omega = 100\pi \).
**Tasks:**
a) Suppose \( x_a(t) \) is sampled at 150 samples/sec resulting in the discrete-time signal \( x[n] \).
- **Task:** Sketch the discrete-time Fourier transform (DTFT) \( X(\omega) = \sum_{n=-\infty}^{\infty} x[n] e^{-j\omega n} \). Label all important values on your sketch.
b) Repeat part a) with a sampling rate of 75 samples/sec.](https://content.bartleby.com/qna-images/question/8b207c38-3ae5-4958-b6f8-8e524b4be30c/8c851d63-0918-49dc-a64e-cc8d9bb1b417/hszmu8_thumbnail.png)
Transcribed Image Text:### Transcription for Educational Website
**A continuous-time signal \( x_a(t) \) has a continuous-time Fourier transform \( X_a(\Omega) = \int_{-\infty}^{\infty} x_a(t) e^{-j\Omega t} dt \) shown below:**
#### Graph Description:
- The graph is a single triangle centered at the origin.
- The x-axis is labeled \( \Omega \) (in rad/sec).
- The y-axis shows \( X_a(\Omega) \).
- The peak of the triangle is at \( \Omega = 0 \) with a maximum value of 1.
- The base of the triangle extends from \( \Omega = -100\pi \) to \( \Omega = 100\pi \).
**Tasks:**
a) Suppose \( x_a(t) \) is sampled at 150 samples/sec resulting in the discrete-time signal \( x[n] \).
- **Task:** Sketch the discrete-time Fourier transform (DTFT) \( X(\omega) = \sum_{n=-\infty}^{\infty} x[n] e^{-j\omega n} \). Label all important values on your sketch.
b) Repeat part a) with a sampling rate of 75 samples/sec.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 4 steps with 19 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Consider the signal x(t) x(t) = sinc (a) Find the Fourier transform of x(t) (b) Determine the bandwidth of the signal (c) Determine the Nyquist rate (d) Sketch the spectrum of the sampled signal xs(t) when: a. fs = 1.5 Nyquist rate b. f = 0.25 Nyquist rate and comment on the result. Which case is corresponding to oversampling? Which case is corresponding to undersampling? When does aliasing occur? P,(t) TW OT sinc 2T Tt +2mp,(w) T sinc 2|t| 1 - TW sinc sinc Tt +27 1 cos(@t) T[8(@ + wo) + 8(@ – w)]arrow_forwardProblem 2. Fourier Transform of the Impulse Consider a unit-impulse signal x(t) = 8(t) а) Find the Fourier Transform, in magnitude and phase. b) Sketch by hand the Spectral Density X(@) and the phase X(@) Explain in words the meaning of these plots. c) Create a MATLAB simulation experiment to visualize that the sum of infinitesimal cosine signals can produce an impulse.arrow_forwardConsider a Fourier series of the following form: f(x) = > in cinkoz 1+n4 Is f(x) a purely real function of r, a purely imaginary function of x, or neither purely real nor purely imaginary? Why or why not?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSON
Delmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage Learning
Programmable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill Education
Electric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSON
Engineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,

Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON

Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning

Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education

Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education

Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON

Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,