Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
5.1-2 Determine the Nyquist sampling rate and the Nyquist sampling interval for the signals (a) sinc² (100rt) (b) 0.01 sinc? (100rt) (c) sinc (100rt) + 3 sinc (60rt) (d) sinc (50rt)sinc (100Tt).

5.1-2 Determine the Nyquist sampling rate and the Nyquist sampling interval for the signals (a) sinc² (100rt) (b) 0.01 sinc? (100rt) (c) sinc (100rt) + 3 sinc (60rt) (d) sinc (50rt)sinc (100Tt).

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
**Exercise 5.1-2: Nyquist Sampling Rate and Interval** Determine the Nyquist sampling rate and the Nyquist sampling interval for the signals: - **(a)** \( \text{sinc}^2(100\pi t) \) - **(b)** \( 0.01 \, \text{sinc}^2(100\pi t) \) - **(c)** \( \text{sinc}(100\pi t) + 3 \, \text{sinc}^2(60\pi t) \) - **(d)** \( \text{sinc}(50\pi t) \text{sinc}(100\pi t) \) **Explanation:** "The sinc function, often denoted as \(\text{sinc}(x)\), is defined as \(\frac{\sin(\pi x)}{\pi x}\). Understanding its behavior and properties is crucial for determining the Nyquist rate, which is the minimum sampling rate to avoid aliasing and accurately reconstruct a continuous signal from its samples. - **(a)** and **(b)** involve variations of \(\text{sinc}^2\) with different scalars affecting the amplitude of the sinc squared function. - **(c)** is a combination of a standard \(\text{sinc}\) function and a scaled \(\text{sinc}^2\) function, indicating different frequency components. - **(d)** depicts the product of two \(\text{sinc}\) functions, suggesting interaction between their respective frequencies. Understanding each signal's bandwidth is key to determining the Nyquist sampling rate, which is double the maximum frequency present in the signal."
Transcribed Image Text:**Exercise 5.1-2: Nyquist Sampling Rate and Interval** Determine the Nyquist sampling rate and the Nyquist sampling interval for the signals: - **(a)** \( \text{sinc}^2(100\pi t) \) - **(b)** \( 0.01 \, \text{sinc}^2(100\pi t) \) - **(c)** \( \text{sinc}(100\pi t) + 3 \, \text{sinc}^2(60\pi t) \) - **(d)** \( \text{sinc}(50\pi t) \text{sinc}(100\pi t) \) **Explanation:** "The sinc function, often denoted as \(\text{sinc}(x)\), is defined as \(\frac{\sin(\pi x)}{\pi x}\). Understanding its behavior and properties is crucial for determining the Nyquist rate, which is the minimum sampling rate to avoid aliasing and accurately reconstruct a continuous signal from its samples. - **(a)** and **(b)** involve variations of \(\text{sinc}^2\) with different scalars affecting the amplitude of the sinc squared function. - **(c)** is a combination of a standard \(\text{sinc}\) function and a scaled \(\text{sinc}^2\) function, indicating different frequency components. - **(d)** depicts the product of two \(\text{sinc}\) functions, suggesting interaction between their respective frequencies. Understanding each signal's bandwidth is key to determining the Nyquist sampling rate, which is double the maximum frequency present in the signal."
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 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