4- Find the Fourier sine and cosine transform of: e-x 0

Q: 10. Solve the following IVP using Fourier Transform: -00 0, u(x,0) = e, -0 <r < oo.

A: Given ut=uxx, -∞&lt;x&lt;∞, t&gt;0u(x,0)=e-x2, -∞&lt;x&lt;∞

Q: 1 (b) Find Fourier cosine transform of f(x)=< -1 <x< 0<x</

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Q: Q8 Find the Fourier transforms of: sin* - pn Sx< pn f(x) otherwise

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Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

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Q: e> and deduce that Find Fourier sine transform of- ar e bx e | sin px dx = Tan2 - Tan a

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Q: 8 The inverse Laplace transform of the function is sin(3t) (A) t – 3 sinh(3t) (B) t- 3 sin(3t) (C)…

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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: e Transform of the functions 1. e2t (

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Q: O Find Fourier Cosine transform of: CoS X oa

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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 ƒ (t) = 2 for -T≤t≤0 2 for 0 ≤ t ≤T

A: We have to solve given problems:

Q: HW: Find the z transform for sin (ak):

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Q: 2. Calculate the Laplace transform L{12e cos²(3t)}.

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Q: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

A: The given problem is to find the Fourier sine transform of the given function, we have a general…

Q: 53. If Fs (n) is the Fourier sine transform of f (x) on 0<x<1, show that 2nt F.[f" (x)] = [f (0) –…

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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: 2Ct-3) Cos Ct-3)

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

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Q: Calculate the Fourier transform of f(x) = (1 – 2)e-(z-a)?/2_

A: Calculate Fourier transform of e-x-a2/2:  ∫-∞∞e-x-a2/2·e-jωxdx=e-jaω∫-∞∞e-x-a2/2·e-jωx-adx-a…

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: 2s²+7 F(s) (s+1)(s+2)(s²+ 2s+5)

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Q: Find the cosine transform of a function of x which is unity for 0 < x < a and zero sin ap , for x2…

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Q: t - 0.2k æ(t) 2.5 1 – 2 Σ rect 0.1 k=-∞

A: Given that, x(t)=2.51-2∑k=-∞∞rectt-0.2k0.1-12 The aim is to find the complex fourier series, The…

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: Find Laplace transform of te-t cos t

A: Using Laplace formulas we will find the Laplace transform of  t e-t cos t

Q: 1 Find the Fourier sine and cosine transform of ƒ(x)=

A: Use the Fourier Sine and Cosine transform table to obtain the result.

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: 2. Use the Laplace Transform table to find Laplace Transform of a) f(t) = sin 2t b) f(t) = e-2t cos…

A: Solution-

Q: 4. e2t+a(2 cos at – 3 cosh 2at) -

A: It is given that the function ft=e2t+a2cosat-3cosh2at. We have to find the Laplace transform of ft…

Q: 2) Find the (complex) Fourier transform of 1-2, if r| S1, F(z) 0. if |피> 1, I COS I- Sin z and hence…

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

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Q: FIND THE LAPLACE TRANSFORM AND INVERSE LAPLACE TRANSFORM dx - + 7 = 5 cos 2t dy -

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Q: Q2/ Find the half-range Fourier sine series representation of the function: f(t) = cos(2t) %3D…

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Q: (b) Find the Fourier-sine transform (assume k ≥0) for 1 f(x) = x + x³

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

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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).

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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: Q.5. Determine the Discrete-Time Fourier Transform and z-Transform of the signal given below. x(n) =…

A: Calculate DTFT: XNk=∑n=-∞∞xne-i2πkNn           =∑n=-∞∞3nu-n-1e-i2πkNn           =∑n=-∞-13ne-i2πkNn…

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: 5 The inverse Laplace transform of the function sin(2t) (A) 1 – 2 sinh(2t) (B) t- 2 sin(2t) (C) t- 2…

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Q: (1, x| a Find the Fourier transform of f (x) defined by f (x) = and hence evaluate

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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: 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: 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: 12. Find the Laplace transform of the period function to f(1) = 2n-t <tS2n

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Q: 4- Find the Fourier sine and cosine transform of: 0 <x < a F(t) = {o otherwise Note: using sin x =…

A: Fourier Sine Transform: Let Fx be defined for x&gt;0. Then Fourier sine transform of Fx is denoted…

Q: Find the fourier transform of f(t) = e-2(t+4)ʻ sin (nt).

A: