1. Use the differentiation and integration properties of Fourier Transform to find a closed form for X(ja). 2. What is the Fourier Transform of g(t) x(t)-;?

Q: . Find the Z transform of : x(k) = (2)*sin,k

A: Z transform

Q: Find the Fourier Sine Transform of e-t and hence find the Fourier Cosine Transform of te-t.

A: Fourier sine transform of e-t is ∫0∞e-tsinωtdt. Calculate it:  ∫0∞e-tsinωtdt=∫0∞e-teiωt-e-iωt2idt…

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: (11) The Fourier cosine transform of the function f(x) e; x>0, is

A:

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

A:

Q: Q4 a) 0, if x 0 1,0 < x < 1 x ≥ 1 b) Evaluate Fourier sine transform of f(x) = {¹,0

A: (a) We have to evaluate Fourier integral representation of the given function. f(x)=0if x&lt;012if…

Q: (b) Find the Fourier transform of the function given below 1– x? if |x|1 and hence find the value of…

A: Calculate Fourier transform: Fω=∫-∞∞fxe-iωxdx         =∫-111-x2cosωx-isinωxdx…

Q: Find the Fourier transform of (a) f (x) = sin (x²), (b) f (x) = cos (x2)

A: 4. Given that,fx=sinx2andfx=cosx2The Fourier transform of the above functions isdetermined as shown…

Q: Derive the general formula for the Laplace transform of sin bt.

A:

Q: 3) Find the Fourier transform of the following signals L. x(t) x(t) + 3 + 2 -2 2 -1 -1 1 -2 using…

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Q: 3) x(t) te-at 1 4) x(s) = (Sta)2

A:

Q: { 1,-< |x| < = (0, anywhere else 2. Find the Fourier transform of the function f (x) =

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

A:

Q: 8. Find the function whose Fourier sine transform is the following function. S[u] - 2 0 x = [1, 2],…

A:

Q: Find the Laplace transform of 4 sin(3t)+2 cos(9t).

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Determine the Laplace Transform of cos*t

A: cos3t≡(cost)(cos2 t) cos3t=cos(1−sin2 t) cos3t=cost⋅1/2(1+cos2t)…

Q: What is the Fourier transform of the following e-j10ntx(t)

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

Q: (1, |x| 15 Q.1 Find the Fourier transform of f (x) defined by f (x) = %3D Hence evaluate S: sins…

A:

Q: 5. Find the Fourier transform of f(x) = 5 if lxl<1 and f(x) = 0 otherwise.

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The Fourier…

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

A: Given function is,

Q: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

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 for S(2)%3D sin a, 2 0.

A:

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

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Q: 3. Find the Fourier Transform of f(t) = 0, - osts0 le-at, osts ∞ a is positive constant

A:

Q: Determine the Laplace transform of L(sinh 5t * cos t)

A: Explanation of the answer is as follows

Q: f(x)= == ¹xcl! Obtain the Fourier transform of

A:

Q: Find the fourier transform of following signals a. x() = cos (2xf.1) b. x(1) = sin (27f 1) c. For…

A: Calculate Fourier transform of cos22πfct: Fcos22πfct=F122cos22πfct-1+1…

Q: Solve the laplace transform of f(t) = sin (10t). Hint: You may convert the given to whichever form…

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Q: 1) Find the Fourier Sine transform of the function f(x) = re %3D

A:

Q: Find the Fourier transform of x(t) shown below using differentiation property * x(t) -1 2)

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Q: The non-periodic function f(x) is defined by f(x) = e-l=l. Obtain the Fourier transform of f(x).

A:

Q: 8. Find the 6th order Fourier approximation of the function that is periodic and f(x) = x, -2<x <2

A: Given function is fx=x ,   -2≤x≤2 Compare the interval  -2≤x≤2 with -L≤x≤L, we get L=2…

Q: 4- Find the Fourier sine and cosine transform of: e-x 0 <x < a F(t) = otherwise

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Q: Find z-transform for the functions (using properties) 1) x(t) = eat cos (w t)

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

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

A:

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

A:

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

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Q: 1: A :Find Laplace Transform of f(t) = sin²t By Rule.

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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: (b) Using Laplace transform, evaluate te -2t Cos 2t dt 0.

A:

Q: Find the Fourier sine transform of (sinx, 0a (2) %3D

A: Fourier transform

Q: Solve for the inverse Laplace transform of O 4cos at - 3 sin at 4 sin at – 3 cos at 3cos at - 4 sin…

A: It is known that: L-1a·fs+b·gs=a·L-1fs+b·L-1gsL-1ss2+a2=cosatL-1as2+a2=sin(at)

Q: transform

A: