3.28. Determine the Fourier series coefficients for each of the following discrete-time periodic signals. Plot the magnitude and phase of each set of coefficients ak. (a) Each x[n] depicted in Figure P3.28(a)-(c) 258 (b) x[n]=sin(2πn/3) cos(πn/2) (c) x[n] periodic with period 4 and πTN x[n] = 1-sin for 0 ≤ n ≤ 3 4 (d) x[n] periodic with period 12 and πn x[n] = 1-sin for 0n 11 4 Fourier Series Representation of Periodic Signals Chap. 3 --- IIIIIIIIIIIII.. x[n] ¨· III. „IIIII IIIII. ¡¡IIII. IIIII IIIII II ¨· -14 -7 0 (a) x[n] 7 LIIIIIII ··· 14 21 n ¨IIIIIIIIIIIIIIIIIIIIIIIIIIII. ¨ -18 -12 -6 0 6 12 18 n (b) x[n] -18 -12 -6 0 6 12 18 (c) Figure P3.28 Problem 6. Consider the DT signal x[n] described in textbook problem 3.28(a), page 257. You only need to consider the signal shown in Figure P3.28(c), page 258. (a) Determine the fundamental frequency w₁ of the signal. (Q35) (b) Determine the absolute value of the Fourier coefficient a_1. (Q36) (c) Determine the absolute value of the Fourier coefficient ao. (Q37) (d) Determine the absolute value of the Fourier coefficient a₁. (Q38) (e) Determine the absolute value of the Fourier coefficient a3. (Q39) (f) Determine the absolute value of the Fourier coefficient ag. (Q40)
3.28. Determine the Fourier series coefficients for each of the following discrete-time periodic signals. Plot the magnitude and phase of each set of coefficients ak. (a) Each x[n] depicted in Figure P3.28(a)-(c) 258 (b) x[n]=sin(2πn/3) cos(πn/2) (c) x[n] periodic with period 4 and πTN x[n] = 1-sin for 0 ≤ n ≤ 3 4 (d) x[n] periodic with period 12 and πn x[n] = 1-sin for 0n 11 4 Fourier Series Representation of Periodic Signals Chap. 3 --- IIIIIIIIIIIII.. x[n] ¨· III. „IIIII IIIII. ¡¡IIII. IIIII IIIII II ¨· -14 -7 0 (a) x[n] 7 LIIIIIII ··· 14 21 n ¨IIIIIIIIIIIIIIIIIIIIIIIIIIII. ¨ -18 -12 -6 0 6 12 18 n (b) x[n] -18 -12 -6 0 6 12 18 (c) Figure P3.28 Problem 6. Consider the DT signal x[n] described in textbook problem 3.28(a), page 257. You only need to consider the signal shown in Figure P3.28(c), page 258. (a) Determine the fundamental frequency w₁ of the signal. (Q35) (b) Determine the absolute value of the Fourier coefficient a_1. (Q36) (c) Determine the absolute value of the Fourier coefficient ao. (Q37) (d) Determine the absolute value of the Fourier coefficient a₁. (Q38) (e) Determine the absolute value of the Fourier coefficient a3. (Q39) (f) Determine the absolute value of the Fourier coefficient ag. (Q40)
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...
Related questions
Question
![3.28. Determine the Fourier series coefficients for each of the following discrete-time
periodic signals. Plot the magnitude and phase of each set of coefficients ak.
(a) Each x[n] depicted in Figure P3.28(a)-(c)
258
(b) x[n]=sin(2πn/3) cos(πn/2)
(c) x[n] periodic with period 4 and
πTN
x[n] = 1-sin
for 0 ≤ n ≤ 3
4
(d) x[n] periodic with period 12 and
πn
x[n] = 1-sin
for 0n 11
4
Fourier Series Representation of Periodic Signals
Chap. 3
--- IIIIIIIIIIIII..
x[n]
¨· III. „IIIII IIIII. ¡¡IIII. IIIII IIIII II ¨·
-14
-7
0
(a)
x[n]
7
LIIIIIII ···
14
21 n
¨IIIIIIIIIIIIIIIIIIIIIIIIIIII. ¨
-18
-12
-6
0
6
12
18
n
(b)
x[n]
-18
-12
-6
0
6
12
18
(c)
Figure P3.28](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c6aa9df-31e2-46b2-bbec-2d2acb2aa6ed%2F1ff33d17-e934-4f3d-a17c-8d27959b2fd0%2Fabgssa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.28. Determine the Fourier series coefficients for each of the following discrete-time
periodic signals. Plot the magnitude and phase of each set of coefficients ak.
(a) Each x[n] depicted in Figure P3.28(a)-(c)
258
(b) x[n]=sin(2πn/3) cos(πn/2)
(c) x[n] periodic with period 4 and
πTN
x[n] = 1-sin
for 0 ≤ n ≤ 3
4
(d) x[n] periodic with period 12 and
πn
x[n] = 1-sin
for 0n 11
4
Fourier Series Representation of Periodic Signals
Chap. 3
--- IIIIIIIIIIIII..
x[n]
¨· III. „IIIII IIIII. ¡¡IIII. IIIII IIIII II ¨·
-14
-7
0
(a)
x[n]
7
LIIIIIII ···
14
21 n
¨IIIIIIIIIIIIIIIIIIIIIIIIIIII. ¨
-18
-12
-6
0
6
12
18
n
(b)
x[n]
-18
-12
-6
0
6
12
18
(c)
Figure P3.28
![Problem 6. Consider the DT signal x[n] described in textbook problem 3.28(a), page 257. You
only need to consider the signal shown in Figure P3.28(c), page 258.
(a) Determine the fundamental frequency w₁ of the signal. (Q35)
(b) Determine the absolute value of the Fourier coefficient a_1. (Q36)
(c) Determine the absolute value of the Fourier coefficient ao. (Q37)
(d) Determine the absolute value of the Fourier coefficient a₁. (Q38)
(e) Determine the absolute value of the Fourier coefficient a3. (Q39)
(f) Determine the absolute value of the Fourier coefficient ag. (Q40)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c6aa9df-31e2-46b2-bbec-2d2acb2aa6ed%2F1ff33d17-e934-4f3d-a17c-8d27959b2fd0%2Ft98fxkb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 6. Consider the DT signal x[n] described in textbook problem 3.28(a), page 257. You
only need to consider the signal shown in Figure P3.28(c), page 258.
(a) Determine the fundamental frequency w₁ of the signal. (Q35)
(b) Determine the absolute value of the Fourier coefficient a_1. (Q36)
(c) Determine the absolute value of the Fourier coefficient ao. (Q37)
(d) Determine the absolute value of the Fourier coefficient a₁. (Q38)
(e) Determine the absolute value of the Fourier coefficient a3. (Q39)
(f) Determine the absolute value of the Fourier coefficient ag. (Q40)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
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
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,