2. Prove the following properties of Discrete-time Fourier transform (DTFT). DTFT DTFT DTFT 1 if x[n] X (e") & y[n] → Y(e") then x[n]y[n]. -| X(eja)Y(e(@-a) )da

Q: 1 (b) Find Fourier cosine transform of f(x)=< -1 <x< 0<x</

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Q: Examine the discrete time Fourier transform of sin) 5nn, .cos( 2 x[n]

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Q: f(t) = SO if 0 c where c> 0.

A: We have to solve given problem:

Q: 8(x – a) + 8(x + a)

A: Topic:- calculus

Q: 4] Find the Laplace Transform of f(t) = { S-1 (-/= + 5 = /₁1) (1te - 1/₁1) (a) (c) S S - I (b) (d) S…

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Q: Use matrix to solve for X(s) and Y(s) in the equations below and find the laplace transform of X(s)…

A: To solve the given problem Simplify for X(s) and Y(s)  Using inverse laplace transformation solve…

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: Find Fourier transform for f(t)=t^3-2t

A: Given function f(t)=t3-2t. To find Fourier transform of f(t). By property of Fourier transform,…

Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: Compute the coefficient Fourier an of the *-1, 0<r <a S(2) = { 0, *<I< 27

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Q: If (p) is the Fourier Sine transform of f(x) for p>0, then prove tha Af(x}} = - (- p) for p<0.

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Q: Confirm that the standard Fourier forward transform of the double-sided decaying exponential signal…

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Q: te Fourier transfor 33 43

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Q: Find Fourier transform of the n-th derivative f(n) of a smooth function f with fast decay at…

A: We know that the Fourier Transform of a function f(x) is possible when the integral ∫-∞∞f(x) e-iωxdx…

Q: 2. f(t) = -7(e^3t)[sinh(2t)] A. -14 / (s^2 – 6s + 5) B. (-7s + 21) / (s^2 – 6s + 5) C. -14 / (s^2 -…

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Q: F{6f"(x) – 2f' (x) + 7f(x)} =

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Q: Find the Exponential Fourier coefficient Cn for signal f(x) = x Defined on interval [-1 ,1]

A: Complex form of Fourier series is defined as follows: fx=∑n=-∞∞cne-inx2πL where,…

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: -21 e * u(t) + e ª u(1)

A: The given function is    e-tut+e-2tut Let xt=e-tut and x1t= e-2tut

Q: Find the laplace transform of H(t) when H(t) = (e^2t-3)(e^2-t)

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Q: Express the half-sine wave load F(t) = sin (2*pi*t) as the Fourier Series and draw a graph (N=10,…

A: Note : As per our policy, we are allowed to answer only first part of question kindly post remaining…

Q: Let f(x) = (x2 + 1), n<x <a be a periodic function, then the Fourier coefficient az = Answer:

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Q: 1. Deduce the continuous function whose Laplace Transform is 10 F(p) P (p² + 9) 2.Find Р2—ЗР+10 (i)…

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

A: We are given the spatial Fourier transform of a spatio-temporal function u(x,t) as : u(k,t) =…

Q: Given that the Fourier transform of e- πt^2 is e- πs what is the Fourier transform of the following…

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Q: Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 1 sin 3(p-1), sin 3(p+1) p-1 p+1 +…

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Q: What is the Fourier transform of 8(x) dx F(k) = 100 = 2T -ikx 8(x) =?

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

Q: Prove that the Fourier transforım of f' (x), the derivative of f (x) is – ip f (p), where S(p) is…

A: Answer: For the given data,

Q: Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz.,…

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