a) Let T(x), n = 1,2,3, ... are the eigenfunctions of the Sturm-Liouville problem; x³y" + 2x²y' + λy = 0, y(1) = 5, y'(3) = 6. Set up the orthogonality condition. b) Write the Fourier-Legendre expansion of the function f(x) = 2x3 - 1.

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Q: Find the Fourier sine expansion of f(x)=x² (3L– 2x) on [0, L].

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Q: [6] Find the Fourier integral representation of f(x) = { 02 0 1.

A: Fourier integral representation

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Q: 4) Find the Fourier transform (FT) of the rectangular pulse signal x(t) analytically by using FT…

A: Find the Fourier transform (FT) of the rectangular pulse signal x(t) analytically by using FT pairs…

Q: ) Compute the Fourier transform of the function. (a) f(x) = h(x + 1) – 2h(x) + h(x - 1), where 1, if…

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Q: . Prove that the matrix A = Cos 0 sin 0 - sin 0 cos - has no real eigenvalues for 0 < 0 < T.

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Q: Find the eigenvalues and eigenspaces for (a) Each of the Pauli operators X, Y, Z;

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 6. (a) Let T: L²[0, 2π] → L²[0, 2π] be given by 2п Tf(x) = -Ĵa cos(xt) f(t) dt. Show that (i) T is…

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Q: is de -Idc 0 K f (at) = { 1 de (b) Fourier coefficient, a If ripple-free load current in…

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Q: true or false prove your answer If (an) is Cauchy and p is a number such that for infinitely many…

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Q: 2) find the fourier transform x(t) = u(t) x(t) ulzt) x²(t) = u(+ + 5) -

A: xt=utxt=u2txt=ut+5xt=ute-jw0t

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Q: [x =3x+2y y = 6x-y

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Q: 0, - 00<t<0 e at, 0<t<∞ Find the Fourier Transform of f(t)={ a is positive constant

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

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

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Q: Q1) using Fourier transform find x(t) below x(t) = [e-3tu(t) * e-6*u(t)] dt

A: Solution is given below

Q: A function f(t) has Fourier transform, F(w) we. What are the Fourier transforms of: (a) f(t-3) (b)…

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Q: Q.3 (a) If F(a) = F{{(x)} is the Fourier transform of f(z), then show that F{f(ax - b)} = Ja where a…

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Q: Use the InverseFourierTransform function of Mathematica or Wolfram Alpha to find the (spatial)…

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Q: Q4. Define Dis crete and Invers Discrete Fourier Trans form? Find the Eigenvalues of the given…

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Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

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Q: Exercise 1 Find the fourier series for the function. a) f(x) = { * if 0 <r< T 27 – if n <a < 27 and…

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Q: Problem 21. Let T(x, y) = (x – y, 3x). Then find all eigenvalues and eigen- vectors of T.

A: The given transformation is:T(x, y)=x-y, 3x

Q: 2 6. The inverse Laplace transform of F(s) = is s+c a) 2e-c (t+b) u (t+b) b) 2e-c (t-b) u (t-b) c)…

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Q: Determine the Fourier transform of the following signal: _(t+1) u(t+1) x (t) = è

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Q: 6. (a) Express the function f(x) = x in on [0, T] as a Fourier cosine series S(x). What is S(-1)?

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