Example 2: Solve for the DTFS coefficient of each fundamental periodic with respective period N of this equation. (2n -k) +5 cos 2n X[k] = 1+ sin (4m + cos k+ E+N) o0 1) o0 +(
Example 2: Solve for the DTFS coefficient of each fundamental periodic with respective period N of this equation. (2n -k) +5 cos 2n X[k] = 1+ sin (4m + cos k+ E+N) o0 1) o0 +(
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...
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Question
Topic: Discrete Fourier Series (DFS)
- Make a detailed explanation of every step and how it works.
![Example 2: Solve for the DTFS coefficient of each fundamental periodic with respective period N of this equation.
2n
X[
x씨 = 1 + sin (wk)+ 5 cos (k) +.
+ cos
-k+
Step 1: Determine the periods of each term and expound to sine and cosine terms.
5
4nk
- e
e
-e
elx – e-jx
elx + e-jx
Note: e° = 1;
sin x =
Cos x =
2j
2j](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ff3db6-fdcc-43a6-b503-deee93f4e76d%2F4395a823-3cc0-45ef-9163-e1058dc19597%2Frratdlo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example 2: Solve for the DTFS coefficient of each fundamental periodic with respective period N of this equation.
2n
X[
x씨 = 1 + sin (wk)+ 5 cos (k) +.
+ cos
-k+
Step 1: Determine the periods of each term and expound to sine and cosine terms.
5
4nk
- e
e
-e
elx – e-jx
elx + e-jx
Note: e° = 1;
sin x =
Cos x =
2j
2j
![Step 2: Simplify the equation and collect/group like terms.
X[k] = 1+ G+)e)*.
-j(2)
e
Step 3: Identify the coefficient from the equation.
: X[0] = 1
1
XI-1] =+ X2] = XI-2) =
x[2] = e X[-2] =e
X[1] =
%3D
2'2j
Note: Each coefficient is identified with a color to match where the value or sample is taken from.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ff3db6-fdcc-43a6-b503-deee93f4e76d%2F4395a823-3cc0-45ef-9163-e1058dc19597%2F5dkgwpi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Step 2: Simplify the equation and collect/group like terms.
X[k] = 1+ G+)e)*.
-j(2)
e
Step 3: Identify the coefficient from the equation.
: X[0] = 1
1
XI-1] =+ X2] = XI-2) =
x[2] = e X[-2] =e
X[1] =
%3D
2'2j
Note: Each coefficient is identified with a color to match where the value or sample is taken from.
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