f(t) = 0, -1

Q: f(t) = e cos2t dt

A: Using properties of Laplace transform we solve the given problem as follows :

Q: Develop Laplace transform of the piecewise continuous function t, 0 ≤ t < 1 f(t): 2-t, 1st < 2 t≥2…

A: The solution is given as

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: Show that the Fourier transform of f (x)= e*/2 is e

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Q: Find the third-order Fourier approximation of f (x) = x, 0 ≤ x ≤ 2π.

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Q: si |x| < a 1. f(x) = [1 0 en otro caso ||

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Q: f(t) = 2 2 (3 cos 6t-5 sin 6t)

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Q: Compute the Fourier transform of the following function: f(x, y) = e-()x-y|+|x+y\)&

A: The given function is, fx,y=e-x-y+x+y The two dimensional Fourier transform is defined by,…

Q: Determine the Fourier transform of the given function: t, 0 < t < 1 0<t<2 f(t) = 2t - 1, 0,…

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Q: Find the Laplace Transform of f(t) = cos t u(t-1)

A: The given function is f (t) = cos (t) u (t – 1):   Find the Laplace transform of the given function.…

Q: What is the laplace transform of f(t) = cos t u(t-1)?

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Q: Find the Laplace transform of 1. f(t) = [1u₂n(t)](2 sint - sin 2t) 2

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Q: Find the Laplace transform of 1. f(t) = [1 − u₂n(t)](2 sin t - sin 2t) - 2

A: Properties of the Laplace transform Laf(t)+bg(t)=aF(s)+bG(s)Lsinat=as2+a2Luc(t)sinat=e-css2+a2

Q: ) Compute the Fourier transform of the function. (a) f(x) = h(x + 1) – 2h(x) + h(x - 1), where 1, if…

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Q: f(t) = u(t− 3)(t - 3)e-4t

A: In this question, the concept of Fourier Transform is applied. Fourier Transform The Fourier…

Q: The Laplace transform of f(t) - t U(t - 3) is:

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Q: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: /Find the Laplace Transform -3 4- f(t) = v2 t re) () = Where r

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Q: Determine the Fourier transform of f(t) = te-2t u(t), where

A: Given ft = te-2tut where ut =0     t&lt;01    t&gt;0 The Fourier transformation is given by Fw…

Q: Find the Laplace transform of 0st<1 f(t) = {2 - t, 1st<2 2 <t

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Q: ): Let y(t) = x(t)*h(t), where x(t) = e-2tu(t) h(t) = e-4tu(t) Compute the Fourier transform of…

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Q: Find the Fourier transform of the following signals using sine and cosine integral. x(t) 1 -1 -1 1…

A: Given function from the graph is: fx=x+1 Fourier transform of a function fx is:…

Q: Compute the Fourier transform of the following function: f (x, y) = e-(1x-y|+|x+y[)<+

A: Calculate Fourier transform: Fu,v=∫y=-∞∞∫x=-∞∞fx,ye-2πjux+vydxdy…

Q: )Find the fourier transform for the function: - 1<t <1 otherwise 1 f(t) = {, | %3D

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

A: Above question is solved.

Q: Find the laplace transform of t sin (t) A. 2s/(s2+1)2 B. 1/s2(s2+1) C. 1/s2 + 1/s2+1 D. -…

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Q: Find the Fourier transform of f(t) = {, t 0 12e-t O 2/(1+jw) O 1/(1+jw) O -1(1+jw) O -2/(1+jw)

A: We have to find the Fourier transform.

Q: Compute the Fourier transform of the following signal: x(t) = e-31e|sin(2t)u(t)

A: The Fourier transform of the function x(t) is represented as X(w), it is defined as ∫-∞∞e-iwtx(t)dt,…

Q: . Show that d(w) cos(Kt). = π[d(w − K) + d(w + K)] is the Fourier transform of -

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Q: -21 e * u(t) + e ª u(1)

A: The given function is    e-tut+e-2tut Let xt=e-tut and x1t= e-2tut

Q: ,determine the Laplace transform of f. Q. f(t)=e2t(1−sin2 t).

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Q: Q2- Find the Fourier Transform for f (t) =A cos o,t, where o, = 2n fo %3D

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Q: Find the Fourier transform of f (x) defined bv f x) = , a 10, > a and hence evaluate sin pa cos dp…

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Q: Find the Fourier transform for f (x) xe c > 0

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Q: (a) Find the Fourier Transform of the function: f(t) = e, for t>0 and a > 0.

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Q: orm of the function f(t

A: Introduction: The formula of Laplace transform of eatcos(bt) is given by, F(s)=(s-a)(s-a)2+b2 The…

Q: x(t) 2 -1 -1 1 -2

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Q: Calculate the Laplace transform of f(t) = 2 cos(3t)

A: The given function is ft=2 cos3t.

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: Obtain the Fourier transform of the double pulse defined by f(t) ={ 1 ,1< or equal to x < or equal…

A: Fourier transform: The Fourier transform of function f is given by, F(ω) = ∫-∞∞f(t) e-ωjtdt. Given:…

Q: Find the Laplace transform of the equation. a and b are constant.

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Q: Find the Fourier transform of f (x) defined by |x| a f (x) = sin? ax ta and hence prove that x2 2

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Q: Find the Fourier Transform F(w) = {e-at t≥0 t≤0

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Q: Given x(t) = 5te-3 u(t), what is the Fourier transform of x(t)?

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: Find the Fourier transform of the given waveform. f(t) -2 -1 1 0 1 2 (s)

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Q: Find the Fourier transform F(@) = | f(t)exp(iwt)dt of the function 0, t 0. You might want to use…

A: The given function is ft=0t&lt;01βtt≥0, where β&gt;0. We know that the Fourier transform of a…

Q: Find the finite Fourier Cosine Transform of f (x), where 0<x <"/3 when f(x) = (x – n when T/3<x<n°

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Q: t, f(t) = 2t - 1, 0, 0 < t < 1 0<t<2 otherwise

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Q: Find the Laplace transform of f(t) = te-t from the definition.

A: Here we use the definition of lapses transformation.