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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)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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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
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.
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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