) Compute the Fourier transform of the function. (a) f(x) = h(x + 1) – 2h(x) + h(x - 1), where 1, if a> 1, 0, otherwise. h(r) = (b) g(r) = e-rlri, %3D

Q: 7 The inverse Laplace Transform of the F(s)==+ is (s-3)

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Q: L-¹ s+2 2s²+4s+ 7

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Q: The Fourier transform of the function f(x)=1 ; |x|<2, is 2 sin 2p (c) F(p)=. 2 sin 2p (a) F(p) = sin…

A:

Q: (a) Find the Fourier transform of the function g: RR defined by Ste-kt, for t > 0, g(t) = otherwise.…

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

Q: 7.1.1. Find the Fourier transform of the following functions: (a) e−(x+4)², (b) e¯\x+¹, x, |x|<1,…

A:

Q: Find the inverse Laplace transform of 1 F(x) S- s2 (s + 1)

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s).…

Q: * Find the inverse Laplace transform for-1 1 F(s) s – 2s + 5 1 -e²"sin2t 2 1,2'sin2t e'sin2t خيار 1…

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Q: 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.…

A:

Q: determine the inverse Laplace transform of F.

A:

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

A:

Q: determine the inverse Laplace transform of F.

A: Given:

Q: 16. The even function f(t) = -t + 1; – 1 <t < 0; f(t + 2) = f(t) has Fourier coefficients -2 ao = 3…

A:

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 a t < 2 a а f(t) = 1 %3D -- 2 < t Whose graph is shown below V t. V

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Q: 5. The fourier transform of the function f(x)=eI, is 2 4- w? O b. 2 w? -4 4 С. w? - 4 Od. 4+w? 4.

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Q: 2. Use the Laplace Transform to solve the following system x'= x-5y, y'=-5x+y, x(0)=1, y(0)=1.

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Q: Derive an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in…

A: The Fourier transform of the function is represented as , it is defined as , where . Since the…

Q: Find the inverse Laplace transform of H(s) -6e-2s s2 – 2s

A:

Q: Find the Fourier transform for x[t] = at*u[t], |a| &lt; 1

A: Given function is,

Q: Compute the Fourier Transform of the following function (3 , –n < x < o (1 , 0<x< TI f(x) =

A:

Q: Find the inverse Laplace transform of Y (s) = + 1(1 - e-**).

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Q: Obtain the Fourier Series expansion of the periodic function f(t): Then, draw the periodic function.…

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Q: 1. Show that the function 2t et cos (et“) is not of exponential order, however its Laplace transform

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Q: Solve the Laplace transform of (1+e-t)2

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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: (2) Find Inverse Laplace transform for; 1 1-F(s)= s(s +1) 3 2-F(s)=- s' +4

A: We need to find the inverse Laplace transform. Part(1) We have 1ss+1 We use partial decomposition.…

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: 4) Derive an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in…

A: Given:

Q: Determine the Laplace transform of the given generalized function. (3*e^(3t))(delta(t-5))

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Q: Find the Laplace Transform of: e-2t sin2t + e3tt2 3t +2

A:

Q: 2. Prove the following properties of Discrete-time Fourier transform (DTFT). DTFT DTFT (a) ifx[n]…

A: Given x[n]⇔DTFTXejω then we have to show x[n-n0]⇔DTFTXejωe-jn0ω=Z(ejω) (say) Proof: we have…

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: Solve the Laplace transform of e-2t cos/3t – t²e-2t

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Q: A- Find inverse Laplace transform of: 2e-5S S3

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

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Q: find the inverse laplace transform of; a)  (S^2+1)/S(S-1)(S+1)(S-2)

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Q: Use Laplace Transform to find the solution of the IVP -y= 1,y(0) = 0 None of the above. e' O e'-1

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Q: 1. Compute the Laplace transform of f(t)= u(t-3)e-²¹ (a) Using a table (ie using one of our…

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Q: 6. у" - у' + 4y %3D 0; у(-2) %3D 1, у'(-2) %3 3

A: We have to solve the given problem by using Laplace transforms.

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

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Q: Taking the z-transform of each term of the second-order eq Yk+2 + a1Yk+1 + a2Yk = Rk gives

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

Q: will rate if correct.

A:

Q: 5. Use the Laplace Transform solve the IVP: x' + y = t (4x + y' = 0 x(0) = 1, y(0) = 2

A: Theory : The Laplace transform of a second order linear differential equation : y" +α y' +βy =f(t)…

Q: (a) Show that the Fourier transform of the function ga(x) := f(ax), where a > 0 is a constant, is…

A: the Fourier transform of f(ax) as a function of the Fourier transform of f(x) is known as change of…

Q: Find the Laplace Transform of f -1 Osx<1 f(x) = 1 x21 2e-s 1 a. 2e-s 52 1 b. 2e-s 1 C. 2e-s 1 d. +

A: We find Laplace transform of given function