x(t) So, (t) = F₁ (t) + F₂ ³ (+1) + P₂ (t).….…..….…... dt = = 28(t + 2) — 28(t− 2) - rect(+¹) + rect( +rect (¹¹) F₁t replace by F₁w F₂ (1) replace by F₂ (w) F2 equation 1. IN Apply Fourier transform, jw F(w) = F₁ (w) + F2₂(w)...... equation 2 F₁ (t) = -8(t+2)+8(t-2)........ equation 3 now t replace by w, F₁ (w) = -2 [+] × 2 F₁ (w) = -4 [c²-e*] F1(w) = 4jwSin²w. and F2 (w) = 2 x 4Sin (2) F₂ (w) = 8Sin (2) F2 (w) = -8Sin2w jw
x(t) So, (t) = F₁ (t) + F₂ ³ (+1) + P₂ (t).….…..….…... dt = = 28(t + 2) — 28(t− 2) - rect(+¹) + rect( +rect (¹¹) F₁t replace by F₁w F₂ (1) replace by F₂ (w) F2 equation 1. IN Apply Fourier transform, jw F(w) = F₁ (w) + F2₂(w)...... equation 2 F₁ (t) = -8(t+2)+8(t-2)........ equation 3 now t replace by w, F₁ (w) = -2 [+] × 2 F₁ (w) = -4 [c²-e*] F1(w) = 4jwSin²w. and F2 (w) = 2 x 4Sin (2) F₂ (w) = 8Sin (2) F2 (w) = -8Sin2w jw
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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