PROBLEM: Derive the z-transform for f(t) = sin oot u(t). z¹sin(@T) ANSWER: F(z) : = 1-2 z ¹ cos(@T) + z-²
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Q: e> and deduce that Find Fourier sine transform of- ar e bx e | sin px dx = Tan2 - Tan a
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Q: Show that d(w) - = [6(w− 1) + 6(w+1)] is the Fourier transform of cos(t). Show that d(w) = −ix[8(w −…
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Q: Find the Fourier transform of f(x) and show details f(x) = {x²² 18 -1<x<0 otherwise
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Q: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…
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Q: Solve equation using Laplace transform ÿ +9y = 6 (t -) sin(t), y(0) = 0, y(0) = 0 %3D
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Q: Prove that Fourier cosine transform of f(x) = cos(x), 0<x<3 is: 1/27 (³ sin 3(p-1), sin 3(p+1) p-1 +…
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Q: Find the function f(x) that has Fourier transform (k) = (1+k4)-1.
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Q: b) Find the Fourier sine transform of f(x) = 12π, 0 < x < 6π
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- Show that ear's co s 2x Ja (log ()+b)) dr-V Dm) Cl,m) B(:0) A(-1,0) Find Fourierexpansion of the function fc) = x2 XE [-T1, TT] then deduce theto = I+ %3D (3)2 (5 '7)? (2) = 24 (2)2 (4)2 (6,2 need 2 answers2. nts) Use the table of Laplace Transforms and 1st shifting theorem to find the Laplace transform of the following functions. (i). f(t) = sinh(t) cos(t) (ii). g(t) = sin² (3t) (iii). h(t) = t· cosh(3t)(a) √ sec¹ (3t) √/tan(3t) dt
- Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 0The inverse Laplace transform is requiredFind the Fourier transform of sinc (2t). (a) 2n A(w/2) 3. (b) п Д(u/4) A(w/8 (d) A(w/16) Moving to the next ouestion.prevents changes to chis anaWerRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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