Home Work1: Find the Fourier transform to the function given below: for t<0 for t = 0 for t>0 -1 1 Home Work2: Obtain the Fourier Transform to the rectangular pulse of duration 2 second and having a magnitude of 10 volts.

Q: 3. Find the Fourier transform of of 1/(1+t²).

A: Let  g(t)=e-at Then g^f=∫-∞∞e-ate-2πiftdt      =∫-∞0e-ate-2πiftdt + ∫0∞e-ate-2πiftdt…

Q: Find the Laplace transform of the following: 1. f(t) = e-2t+5) sin³(8t) 3

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Q: N= 20 , a= 6 a. Find the Fourier Transform of the constant function f for f(x) = N, 0<x < N (Note: N…

A: Given N=20 and a=6 Since Fourier transform of f(x), -∞&lt;x&lt;∞, denoted by F(ω) where ω∈N, is…

Q: Q1: A: Find the Laplace Transformer for the following function [8 sin²t cos²t] t L

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Q: Find the Fourier transform of each function. In each case, a is a positive real constant. Answer:…

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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: 1. Problem Solving. Solve the following problems completely. Use additional short coupon bond for…

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Q: What is the inverse Laplace transform of the attached function, expressing the answer as f(t), using…

A: Step 1:Step 2:Step 3:Step 4:Step 5:

Q: V(t) A T/4 -T/4

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Q: Find the transforms of the given functions: Please see attachment

A: By the properties of Laplace transformations:

Q: i). ƒ (t) = ²) ² ii). ƒ (t) =t²sinh (21) (5–31

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Q: Find the Laplace transform of the following: 1. 4t + 12 2. 1.5 sin(3t-3)

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Q: S(1) = >1

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Q: Suppose the function f: R→ R has Fourier transform 1 f(p) = e-p². 1+ 4π²p² i. What is the Fourier…

A: As per the question we are given the Fourier transform of a function f(x) as f̂(p) From that we have…

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: -3iw sin 5w 20e F(@) = %3D 3

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Q: Q4: Find the inverse Fourier transform of the spectrum: - 2s w S0 X (w) = 0 swS2 -- 0.W EIN I 0

A: Definition:

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

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Q: Write the general equations for the following: a. Laplace Transform b. Fourier Transform

A: The Laplace and Fourier transformation are two important integral transformations with kernel one.…

Q: How to solve the Laplace transform of the following equation: W(t)=cos(3t) - cos(7t) Please write…

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Q: A gate function (square pulse with magnitude of 1) is centered at the origin and ha width of 2…

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Q: Q5) Find the Fourier transform of: SCos(nt/t) for lel < x(t)=D .elsewhere) Sketch X(f) versus f.On…

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Q: Laplace transform of the following functions: 2. t5/2 sinh 4t

A: We find the Laplace transform of the given function in Problem 2

Q: Example Find the Fourier transform of the rectangular pulse duration T and amplitude A T T SC) = 4…

A: The given problem is to find the Fourier transform for the given rectangular pulse function.

Q: Find the Laplace transform of the f(t) = 8t° e2t – 3t cos(t) + 10. Explain the solution steps in…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 2. Find the transform of the equation x² + xy + y² = 1 when the…

A: Let us consider the equation to transform the coordinate use  x=Xcosθ-Ysinθy=Xsinθ+Ycosθ

Q: Note:M=13 1. Find the Laplace transform of the function: f (t) = eMCosh(Mt) – Msin³ (t) + M sin(Mt)…

A: given function ft=eMt CoshMt-Msin3t+M sinMtcost here  M=13 thus, ft=e13t Cosh13t-13sin3t+13…

Q: .2 TX e cos(x)

A: Given, fx=e-πx2cosx ∴ℱfx=f~p=12π∫-∞∞eipxfxdx⇒ℱe-πx2cosx=12π∫-∞∞eipxe-πx2cosxdx…

Q: · findd the fourier sine transform of f(x) = 7 A 9x 0<X<9 otherwise

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Q: 1. Find the laplace transform of 2e^(3t) sin 4 t 2. Simplify i²⁹ + i²¹ + i 3. Write in the form a…

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Q: Sketch the following waveform f(t)=V₁ -t/2stst/2 = 0 otherwise and show that its Fourier transform…

A: The waveform is given as follows:.We need to find its Fourier transform.We know that the Fourier…