A function f (t) = e-at is defined for a > 0 andt > 0. By finding the Fourier transform show that making the substitution s = jw in the Laplace transform of f results in the Fourier transform. The Laplace transform can be taken from the table.

Q: Find the Fourier transform of d(t – 2). (a) ej2w (b) e-j2w (c) ejw (d) d) e-jw O (d) Moving to…

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Q: Ql- Find y(2.1), x(2.1) for the following first-order simultaneous differential equations by…

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

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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: 2. Determine the inverse Fourier transform of the following functions: a لمند 2// 1 ـ لما

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Q: Find the Fourier transform F(e-az) of f(x) = e-a if x > 0 and f(x) = 0 if x 0.

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Q: -i 5.8.2. (a) Evaluate the discrete Fourier transform of -1 1 i (b) Evaluate the inverse transform…

A: Solve each using the properties and method of determining discrete Fourier transform and inverse…

Q: Compute the Laplace Transform of f(t) e-St using the definition of the transform. (Just listing the…

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Q: Let f(t) = e^t if 0=1   Write f(t) using step function and find the laplace transform. Also,…

A: We have to write f(t) using step function and find the laplace transform. Also, draw the graph.

Q: Find the Fourier Cosine Transform of the function -mx f(x) = (ae-m +be¯¹x}³_if_x>0 if a = 5, b = 4,…

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Q: x) = {0 ² ². 0, Determine the Fourier transform of the function: f(x) 0<*? x<0

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Q: What is the Inverse Fourier transform of: F(w)=, (w+6) Your answer should be expressed as a function…

A: To find inverse Fourier transform of Fw=-46+iw3 , we can use some standard Fourier transform…

Q: Find the Fourier transform of f(x) and show details f(x) = {x²² 18 -1<x<0 otherwise

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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: 2) There is a function F (s) with "different true root state". Make the inverse laplace transform of…

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Q: Use direct integration to find the Fourier transform G(f) of signal

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Q: Compute the Fourier transform of the following function: f(x) = e-a(r-x0)²+iqx (5) where a > 0 and q…

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Q: Find the Fourier Transforms of the indicated function: f (x) = e-3x for x > 0 and f (x) = e2x for x…

A: We have,fx=e-3xx&gt;0e2xx&lt;0 To Do: Find the Fourier Transform of the given function.

Q: (1) Develop a first order method for approximating f′′(x) that uses data f(x− h),f(x),f(x+3h) only.…

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Q: Find the function f(x) that has Fourier transform (k) = (1+k4)-1.

A: Here we have to find out  .Now from definition of inverse fourier transform , to evaluate this…

Q: a. Determine the formula for the Laplace transform. et sin 5t-t³ + e 2t) = (Type an expression using…

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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: -Obtain the Fourier transform of f(t): = sin (30) -t²+7it+12

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Q: Determine the Fourier transform and plot the magnitude S1, It| < T/2 l0, otherwise (ii) x(t) = f(x)…

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Q: 2-find the laplac transform for the function: t² (u-1)

A: Introduction: Laplace transform is named in honour of the great French mathematician, Pierre Simon…

Q: Find The Fourier Transform for the signal Given y-Cosht

A: Given: Signal, y=coshtTo find: Fourier transform of the given signal.

Q: Find the fourier Transform for the signal Given Ye Sinh (H)

A: Given: Signal, y=sinhtTo find: Fourier transform of the given signal.

Q: Find the Fourier transform $\tilde{f}(p)$ of the function 4x²e-5¹ for x ≥ 0 for x < 0. f(x) = {…

A: fx=4x2e-5xfor x≥00for x&lt;0

Q: npute the Fourier transform of 2e33rt/2sinc(t/3 – 4)

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Q: Show how to do the Laplace transform of f(t) = t*cos(w*t) using the table of operational transforms.

A: Given  f(t) =t cos ω t

Q: Find the Fourier Transforms of the indicated function: f (x) = xe-|x|

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Q: What is the Fourier transform of: f(t)=sgn(t) e? Your answer should be expressed as a function of w…

A: Given a function ft=7i2sgnte−8t Explanation ft=7i2e−8t       for t&gt;0 ; t&gt;0 sgnt=1−7i2e8t…

Q: Find the Fourier Cosine Transform of the function ƒ(x) = (ae-4x + be-³x + ce-²x)² if x > 0 if a = 4,…

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Q: Find the Fourier transform of f(t) = [Aeat ]u(t) %3D and draw the amplitude and phase spectrum

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