1 The Fourier transform of [e 2 x(t + )] is jt 1 jn( f- X(f)e#ft X(f – e"(s-±) 4 t A. O . A. X(f)e2#ft X(f - *

Q: Find the inverse Laplace transform of (i) using Residue theorem. (s+3)(s²+5s+6) (ii) using…

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Q: 4. Find the inverse z- transform of the following 3 de XCZ)= tanh (z-)

A: Given: Let us find the inverse z-transform of the given following, xz=tanh-1z2-14

Q: If f(x) has the Fourier transform F(p), then f(x) cos ax has the Fourier transform [F(p-a) + F(p +…

A: If Fourier transform of f(x) is F(p), then we have to prove that the Fourier transform of f(x)…

Q: 5.68. Find the inverse Fourier transform of 1 X(w) = (a + jw)™ Hint: Differentiate Eq. (5.155) N…

A: Given: To find the Inverse Fourier transform of  X(ω) = 1(a+jω)N

Q: -kx (b) Find the Fourier integral of the function f(x) = e when x > 0 and f(-x) = f(x) for k>0 cos2x…

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Q: 1. Find the Fourier transform of this rectangular pulse X (w) and show that sin πωτ X(w) = A² 2.…

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Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: Q4) Find Z transform for the functions 3) x(t) = te-at

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Q: 4) Consider the square wave function f(x) = { 1, 0 <x<n -1, T < x < 2n a. Find the Fourier series…

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Q: 3. Find the Fourier transform of the following: f(t) = {te-t -1<t<0 elsewhere

A: We have to find the Fourier transform of the given function.

Q: 2 The inverse Laplace transform by using integral of transform s(s2 +2s+4)

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Q: The Laplace transform L{e^-t^2} exists (because it is exponential order), but without finding it…

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Q: 2 (b) Find the inverse Laplace transform of by using s(s2 + 2s + 4) (i) Partial fraction (ii)…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2s2 +13s+6 Find the inverse Laplace transform of H(s) = (s+2)2(s-1) assuming that a) h(t) is causal…

A: We will find out the required inverse Laplace transform of H(s)

Q: 3. Find the Fourier Transform of a t < 2 a а f(t) = 1 %3D -- 2 < t Whose graph is shown below V t. V

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Q: (a) Consider a continuous-time signal g(t) with its Fourier Transform as below: (2 sin(w) G(jw) =…

A: Given equation is, Gjω=1-e-jω22sinωω+e-jω3 We have a recttT⇒2AsinωT2ω Let, A=1, T=2 then…

Q: 2s²+7 F(s) (s+1)(s+2)(s²+ 2s+5)

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Q: S1 -x, xl 1 Find the Fourier transform off(x) = and hence evaluate sin x) Cos 2 X COS X – dx.

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Q: Using Fourier transform to solve the following IVP U=2 u+te-lxl, -0 0 XX u(x, 0)= f(x) u,(x, 0) =…

A: Given: utt=2uxx+e-x;               -∞&lt;x&lt;∞ and t&gt;0 u(x,0)=f(x) ut(x,0)=g(x) utt=2uxx+e-x;…

Q: 1 Find the inverse Laplace transform of X(s) = given ROC: -1<o<3. (s + 1)(s – 3) x(t) =

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Q: (d) Show that the Fourier transform of a Gaussian is a Gaussian, and hence show that eik dk 2πδ(x).

A: The Dirac delta function is one of the most significant functions in mathematics. It is widely used…

Q: of the function. 4. Find the Fourier transform of of 1/(1+t²).

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Q: Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal x(t) with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Which of the following is the Laplace transform of the solution to the initial value problem x" + a'…

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Q: Find the Laplace Transform of e 2 cos3t + 5e 2 sin3t - s+2 + s2+9 15 A. g²+9 (s+2) + 15 (s2+4s) + 13…

A: To find the laplace transform of given function first we will use the linearity property of laplace…

Q: Find Laplace transform of R) =-t+1#0st<1 OA 1 es OB 1 1 es OC. 1 1 OD Non of the above. OE 1 1 e-s…

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Q: 7. Find the Fourier sine and cosine transforms of the following functions defined on [0, ∞). x =…

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Q: d the Laplace Transform of the periodic function f(x) 5 for 0<r < 7 T0 for 7<r< 14 s(1–e-14*) 5(e-78…

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Q: Find the Laplace Transform of e-t sin2t 2 2s 2 A. ²/+ B. S (s+1)²+4 (S-1)²+4 C. S+1 s(S²+4) D. None…

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Q: (i) Find the Laplace transform of e" sin 21 dt (ii) Form the PDE by eliminating arbitrary constants…

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Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: 1. Compute the Fourier transform of the following signal: x(t) = e-3|t| sin(2t)u(t)

A: Hint: The convolution theorem of Fourier transform states that, the Fourier transform of the…

Q: Give the Laplace transform of -4 x- 3 0 <x and x < 2 (x) = 2 2 <x 2 F(s) 1 3 + -2s +e 2 2 +e + -2s 2…

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Q: Give the Laplace transform of -2x 0Sx and x < 3 f(x) = 4 3<x -3s 27 20 O F(s) = -- b) O F(s) = - -3s…

A: Solution :-

Q: 7 Find the inverse Laplace transform of using Residue theorem. (s+3)(s²+5s+6)

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Q: 1.) Give the Fourier transform of the function f. Sx ha x = [0, 1] f(x) = 0 otherwise.

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Q: Find laplace transform of x" + 3x' + 2x = t(e^(-t)) Where x'(0) = 0 , x(0) = 1

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Q: 1. Consider the function [x-1, f(x) = 0, (1.1) Find the Fourier transform of f(x). if 0 ≤ x ≤ 1,…

A: For part 1.1, we are given the function f(x)=x-1,           if  0≤x≤10,                  elsewhere…

Q: (7) Find the Fourier transform of the following functions: { {: cos x, if 0 1 (ii) f(x) = 0,

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Q: a Find the Fourier transform of the signal x(7) = 2 cos(m)[(1+3)-(1-3)], using the Fourier integral.

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Q: 1. Find the Laplace transform of f(t) = (t-3)u,(t)-(-2)u,(t). (s-3)e2 s +6s +13 2. Find inverse…

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Q: b

A: From the given statement, the functions are

Q: 1 (iv) If f(t) = e2ºH(t), its Fourier transform is F(@) = -2+iw

A: In this question we have to find whether it is true or false.

Q: will rate if correct.

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Q: If the exponential Fourier transform of f (x) = e-alxl 2a %3D a2 +b2 What is the Fourier transform…

A: considering the function fx=e-ax=2aa2+p2   fx=e-ax=2aa2+p2 and fx=e-bx=2ba2+p2

Q: H.W: Obtain Z-transform for the Followings 1) x(t) = Coswt 1 2) x(s) (s+a)? 1 3) x(s) = s(s+1)

A: We have to use standard z transforms.

Q: 54. If Fe (n) is the Fourier cosine transform of f (x) on 0 < x < 1, show that Fel8" (=)) = }(-1)"…

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