Find the Fourier transform for x[t] = at*u[t], |a| < 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: . Find the Z transform of : x(k) = (2)*sin,k

A: Z transform

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: 4 Find the Fourier Transform of f(x) where S(x) =e*

A:

Q: Find the Fourier transform off (x) defined by Example 6. 1, |x| a f(x) = sin s ds (ii) 00 sin sa.…

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

A:

Q: The Laplace transform of d3x(t) / dt3 is given by?

A: To find Laplace transform of d3x(t)dt3

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: What is the initial value of f(t) if its Laplace transform is 5-2? 2s(s+2)

A: To Find: The initial value of f(t) if its Laplace transform is s-22ss+2

Q: Find the Z transform of [cos (ax), x20 f(x)=: 0, x<0

A: Given, fx=cosax,x≥00,x&lt;0 As we know that, Ze-ax=1+e-aτ+e-2τz-2+...=11-e-aτz-1=zz-e-aτ

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

A:

Q: Find the finite Fourier Cosine Transform of f(x) = 1- in (0, x).

A:

Q: What is the Laplace transform of x(t) = e-tcos(pi)t?

A: To find the Laplace transform of ,  x(t) = e-tcos πt Here the proof for standard form has been…

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: Find the Laplace transform of u2(t)cos(t − 2)

A: This is laplace transform shift problem

Q: Find Inverse Laplace transform of this -{in (1 + #)}' where c is a constant.

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Q: determine the inverse Laplace transform of F.

A:

Q: 7) Use the Laplace transform method to solve the Volterra integral equation: u(x) =1-x - (x -t u (1…

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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. -…

A:

Q: Find the fourier sine transform of a) f(x) = exp(-ar) and deduce sin(sz) -ds = 2+a² -az b) f(x)= re'…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Find the Fourier Transform of Hence Prove that f(x): cos(sx) + Ssin(sx) 1+s² -ds = x 0 OEIN 0 2 Tex…

A: Introduction: Through Fourier transformation, a real-time function can be converted into a complex…

Q: Find the Laplace transform of f(t) = t2 cos at. %3D

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Q: The Fourier transform exists when the Fourier integral in Eq. (18.8) converges. A sufficient but no…

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

A:

Q: Obtain the z-transform of the following: x(n)=na" sin(an)u(n)

A: Let us start solving the problem step by step.... We need to find the z-transform of x(n)

Q: Find the laplace transform of f(t)=t^n by definition.

A:

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

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Q: f(x) = = 1 2 cos: X x

A:

Q: Find the Fourier Transform of Sa? – x², for |æ| a f(x) = and hence deduce that (sin s- s coss -) ds…

A: Fourier transform of gx=1 for x&lt;a0 for x&gt;a is ∫-aa1.e-isxdx. Calculate it:…

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

A:

Q: (a) By making appropriate use of Jordan's lemma, find the Fourier transform of T³ f(x) = (x² + 1)²*

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Q: f(t) = cos² 2t

A:

Q: Find the Fourier transform of the function : S (t) = e-x2 %3D

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Q: Compute the Laplace transform of f (t) = te^−3t directly from the integral definition

A: The Laplace transformation is an integral transformation. When a function is piecewise continuous…

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 the Laplace transform of the given function; a and b are real numbers and n is a positive…

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

A: The given function is ft=2 cos3t.

Q: 1. Prove the scale change theorem on the Laplace transform, that L[f9) = aF (as)

A:

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

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Q: Solve the Laplace Transform 8. f(x) = (2/x)(cos1/2x)

A: note : We will consider the given function as : f(x) = (2/x) cos(0.5x)   Now we have to find the…

Q: x(t)=1(t+4T)

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°

A:

Q: 4. Determine the Laplace transform of the Laguerre polynomials, defined by et dn Ln(t) : ni din…

A: Solution:

Q: 2. The laplace transform of f(t) = et

A:

Q: Find the Fourier Transform of f) = { - z - n<x< 0 0 <x<T

A: We have to find the Fourier Transform 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

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

A: Here we use the definition of lapses transformation.