If F(s) is the complex Fourier transform of the function f (x), then prove that F{f (x – a)} = e-ias F(s).

Q: If the function of is odd function (i.e. f(-x) = - f cx)) then, the Fourier transform of f(x) is…

A: Introduction: The Fourier Transform may be used to deal with preliminary boundary cost problems at…

Q: 9. The most economic form to determine the Fourier coefficient a,, for the function f(0)=0² in the…

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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: Answer #5 and find the Inverse Laplace Transform of the functions by reduction to partial fractions.…

A: 5. The given Laplace transformation is                              s2+5s-2s+12s-1s-7

Q: Here is the graph of the Function f (x) = |x| and a transform of the graph %3D 4 -4 -2 2 4 6 -2 What…

A: This question is related to functions and transformation, We will solve it using given information.

Q: -kx (b) Find the Fourier integral of the function f(x) = e when x > 0 and f(-x) = f(x) for k>0 cos2x…

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Q: - 34 as f(4)= ė" ult-1) Solve it in fourier transformation

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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: Question: Find the Fourier transform of 1. F(e**) 2. е 2 -a 2

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Q: Use Laplace transforms to solve the following initial value problem. x(3) +x"- 42x' =0, x(0) = 0,…

A: Solution of given differential equation by using Laplace transform is given as follows

Q: Q3/ Find Fourier cosine transform of the function f (x) = 2x ,0 < x < 4

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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: Determine the Inverse Laplace Transform of the functions using the Laplace of Integrals and…

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Q: 3. Solving the following problem using Fourier transformation method. du d²u a² -= 0, (t> 0, -∞0 < x…

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

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Q: f(x) = e2* if x> 0 Q5. The Fourier transform of the function: 0 if x<0]

A: We have given a function ,  fx = e-2x , x &gt; 00        ,x &lt; 0 We need to find Fourier transform…

Q: Question 1 Evaluate the following integrals using residue theorem: (a) L (2² +9) (1 dz (x²+9)(x²+4)²…

A: You have explicitly written on the top of your question post that you want only Question 1 to be…

Q: (2 0<x<1) = }4 1<x< 2 l6 2<x<3) 1-for the function f(x) a-Draw the function. b-Represent it with…

A: As per our guidelines we are supposed to solve only one question. Please repost the other questions.…

Q: 2s3+ 4s²+1 F(s) = (s²+ 2s+17)(s²+ 4s+20)

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Q: 2s²+7 F(s) (s+1)(s+2)(s²+ 2s+5)

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Q: COS TA sin a da 1- cOS Ta sin πα da 4' 2

A: The Fourier sine-transform is the imaginary part of the full Fourier Transform. If f(x) is an odd…

Q: 13 5. In the process of calculating the inverse Laplace transform of the function F(s) = -27- arctan…

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

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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: 2)Find the fourier transform for the function 0 <t < 2 1 f (t) = {0 %3D otherwise

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

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Q: The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t = tan(x/2)…

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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: Find the Fourier transform of e 2

A: For the solution follow the next step.

Q: Find the Laplace transform of the following functions as a function of "s" and simplify your final…

A: Given function is  ft=3sin bt cosh bt By definition of Laplace transform Lft=∫0∞e-stftdt

Q: 7. In the process of computing the inverse Laplace transform of the function F(s) = -23 - arctan ¹…

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Q: find 2d Fourier transform of e^(-4pi*(x^2+y^2)) the answer is e^(-pi(x^2+y^2)/2) why?

A: Find the 2d Fourier transform of the given function and the 2D transform of f is defined by the…

Q: Find Fourier Sine and Cosine transform of the function f(x) = e -x

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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: x2, Ixl a

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Q: b

A: From the given statement, the functions are

Q: 1. Find the Fourier transform of the following functions, and verify your results by com- puting the…

A: Use the properties of Fourier transform to determine it. Apply the properties and simplify to get…

Q: Suppose you're given the following Fourier co- -2 a3 9. -2 -3 a2 27 -1 1 efficients: ay 2 b3 2n' 3…

A: Fourier series is an infinite series that includes sine and cosine function. These two functions are…

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: 1. g(t) 3D 4x(t)e/2n4(0) + Зу(t) 2. g(t) = 2y(t) 3. д(t) %3D х(t —2)у(4t) 4. g(t) = 8(t) * y(t) dt

A: Fourier transformation is given by: x(t)=X(f)y(t)=Y(f) 1.)   g(t)=4x(t) ei2π4t+3y(t) Apply Fourier…

Q: 1 Find the Fourier CosineTransform of the function f(x) 1+x2

A: We have to find the cosine transform of the given function.

Q: 10. If it is known that the periodic function f(t) contains even harmonics only, which Fourier…

A: Let us consider a function f(x)  in the interval [-L,L] such that function is an even periodic…

Q: 5(a) Find the Fourier transform for the following function: f(t) = {e-31 0 . t> 0 ,elsewhere

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Q: Use Laplace transforms to solve the following initial value problem. x(3) + x" - 6x' = 0, x(0) = 0,…

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Q: 5. Solve the following initial value problem: (You do not need to find the inverse Fourier…

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Q: 2s+3 5) Find the inverse Laplace transform of F(s) = %D (s+1)(s2+9)

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.