{4^t. ne condition on B for the MA(1) to be invertible.

Q: lon of mtegradoM Sthe nte Shitch the and evaluate -2T -T

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Q: Find all real values of 0 such that cos 0 – sin 0 sin 0 cos 0 has real eigenvalues.

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Q: Find the fourier transform of the following. functions by making use of Jordan's Lemma. a) 1 (x² +…

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Q: Using above basis set, show that these basis functions are eigenfunction of Å = What is the…

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

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Show that f is an eigenfunction of L². What is the eigenvalue?

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Q: Find the complex transform of F(x) = e¬l\l, –∞ < x < ∞

A: Complex Fourier Transform or Fourier Transform: Let Fx be a function defined on R Then Complex…

Q: 1. Let F : L² (R¹) → L²(R¹) be the Fourier transform. That is: 1 F(f) = = √e-i(+1) e-i(x,x) f(x) dx.…

A: Problem is solved using concept of Fourier Transform.

Q: Consider the function f(x)= e-ax² where a is a positive, real constant, and the operator d² B= -4x².…

A: (a) The given function is fx=e-ax2, where a is a positive real constant. The given operator is…

Q: Find Laplace transform of the function f(t) cos(4t + 5) + e-tu(t – 6) + tcosh²4t

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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 laplace transform of the following. 1-) f(t) 3 3U(+) + = 2.) fl+] 3.) h(t) = + 8(+-2) +…

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Q: 4) Which of the following functions are eigen functions of the operator dx ? Show your proof. a) eax…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Use the eigen method and another method to find the GS of coS |X + sin X' =

A: Use the eigen method and another method to find the GS of  X'=1-21-1X+cos(t)sin(t)

Q: Obtain the Fourier expansin f I+ 9X în -3 LXLO 3 f(x) = %3D 3.

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Q: 6) Find Fourier transform of: 8 88 e-n(y² +y) (x −y)e¯\x-y\dy 2) f nye-ny² dy

A: Given Data: To find the fourier transform of given  2)  ∫0xπye-πy2dy

Q: = {H (x-2)} = √I (TTK + SCI)) H Heaviside function S→ Dirac delta function

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Q: Suppose that f: R-Cis a measurable function with 1+ |xf° for almost all x E R. Show that its Fourier…

A: Let, f⏜ be Fourier transform of fx. Then nth derivative of f⏜ is Fourier transform of…

Q: If g(t) has Fourier Transform G(), show that g (t) has transform G (-a).+

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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

Q: Students in an experimental psychology class did research on depression as a sign of stress. A test…

A: Students in an experimental psychology class did research on depression as a sign of stress. A test…

Q: Q5/Determine the Laplace inverse transforms of 3s+s+12s +2 (s -3)(s+1)

A: Please see the explanation below

Q: Obtain the inverse Fourier transform of sen(4(w+2)) (w+2)(3-((w+2)) F(w) =

A: The given function is Simplify the expressions using partial fractionsMultiply both sides of the…

Q: Show that x(t) * u(t) x(t)dt %3D and find its Fourier transform.

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Q: -at² - 2 @ Show: Sē jeate dt - 17€ е = a 2 -at 1 Find the Fourier Transform of f(t) = ē

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Q: The Fourier Transform of * x(t) = [u(t)-u(t-2)][u(t) – u(t − 1)] 8(t - 0.5) cos(2πt) - O exp(j0.5w)…

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Q: The Wigner-Weyl transform is given by 1 W (r,p) 2nh a) Proof that V(2)* = / dp W (z.p).

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

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: Find the Fourier transform of -et +2 cos(t). (a) -27 8(w+ 1) (b) 2n 8(w + 1) (c) -27 8(w- 1) (d) 2n…

A: To solve this problem we use the following the results and formula:

Q: Which of the following is True about the Fourier transform of the signal x(t) = u(t) — u(−t)? - X(w)…

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Q: (2) Transposition.(a) Illustrate (AB) = BT AT by simple examples. (b) Prove (AB) = BT AT

A: We have to prove (AB) T = BT AT . By example and then by proving it for general.

Q: Which of the following are eigen functions of the operator d2/dx2 , find the corresponding eigen…

A: Calculate:  d2dx2sinx=-sinx.  Thus, sinx is eigen function with eigen value -1.

Q: 3. Find the inverse Laplace transform. a) 8s2 − 4s + 12/s(s2 + 4)

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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: Σ (TI, (3=})) – nln(0) – Find the maximum likelihood .0 estimate of 3/E1 i n n i=1 V V E,

A: As logL value is given in the question so we can find the MLE of Theta by partially diff. LogL and…

Q: x(^) = x³ + X² +A+2 x(^) = x³ + x² +A+1 x(A) = X³ + 2A² + A + 1 x(^) = 1³ + A +1

A: This is a problem of stability and linear transformation.

Q: Find invertible representation of Y, = 0.9Y;-1 + e; + 0.5e;-1

A: Given: time series AR(2) process  Yt=0.9Y(t-1) +et+0.5 e(t-1) Then find invertible of Yt?

Q: (-1)"–1 n2 2 1

A: