Problem 3: Consider signal At) = sinc²(50zrt). (a) Find the Fourier transform of At). (b) Based on its Fourier transform, calculate its bandwidth and its Nyquist sampling rate. (c) Signal (t) is sampled with sampling rate 300r rad/s (or 150 Hz). Design an ideal low pass filter that can recover the original (unsampled) signal perfectly.

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...
icon
Related questions
icon
Concept explainers
Question

Help me please

Problem 3:
Consider signal (t) = sinc²(50zxt).
(a) Find the Fourier transform of At).
(b) Based on its Fourier transform, calculate its bandwidth and its Nyquist sampling rate.
(c) Signal At) is sampled with sampling rate 300x rad/s (or 150 Hz). Design an ideal low pass filter that can
recover the original (unsampled) signal perfectly.
(d) To recover the original signal from the sampled signal in (c), we can use a low-pass filter. Now, think about
using a Butterworth filter with half-power frequency @, = 200z rad/s to achieve this. To ensure desirable
filtering behavior, we want the filter to satisfy:
|H(jm)| 2 0.95 at o = 150z rad/s.
• [H(jo) < 0.05 at o = 400x rad/s.
Calculate the smallest order n of the Butterworth filter that can satisfy the above criteria.
(e) Find all the poles of the resulting Butterworth filter in (d).
Transcribed Image Text:Problem 3: Consider signal (t) = sinc²(50zxt). (a) Find the Fourier transform of At). (b) Based on its Fourier transform, calculate its bandwidth and its Nyquist sampling rate. (c) Signal At) is sampled with sampling rate 300x rad/s (or 150 Hz). Design an ideal low pass filter that can recover the original (unsampled) signal perfectly. (d) To recover the original signal from the sampled signal in (c), we can use a low-pass filter. Now, think about using a Butterworth filter with half-power frequency @, = 200z rad/s to achieve this. To ensure desirable filtering behavior, we want the filter to satisfy: |H(jm)| 2 0.95 at o = 150z rad/s. • [H(jo) < 0.05 at o = 400x rad/s. Calculate the smallest order n of the Butterworth filter that can satisfy the above criteria. (e) Find all the poles of the resulting Butterworth filter in (d).
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Thermistors
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
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,