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

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: 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: 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: f(x) = [sin x if 0 T

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Q: 3. Let f(x) = x sin(x) on [-7,7]. (a) Write a Fourier expansion of f(x) on this interval. (b) Use…

A: The given function is fx=xsinx on -π,π.   The Fourier series for a function fx defined on the…

Q: Ost< 2H 3. fe)= (-sim( 못) , 플스. %3D

A: The Fourier series of function f(t) will be given by f(t)=a02+∑n=1∞ancos(nx)+bnsin(nx). Where,…

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: 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: The Fourier Cosine transform of the function f(X) = {1, |x| a} a A 1/(/2n)*(cos(as)/s) B…

A: Given functionfx=1,x&lt;a0,x&lt;aFourier cosine transform of f(x) is given byFcfx2=2π ∫0∞ f(x)…

Q: The complex exponential Fourier coefficients for the periodic function x(t)=t, 0<t<2 is:

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Q: Consider the function f(x) = cos(2x) for -2pi &lt; x ≤ 2pi and zero otherwise.A) Show that it meets…

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Q: find Fourier coefficients

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Q: For the following signal: f(t) = 2 for -2n < t < 0 = -1 for 0 < t < 2n a) Plot the signal by hand.…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let f(x)=2 cos(5x)+3 sin(4x) and let q, be the Fourier polynomial of degree n for f. (a) Show that…

A: Given: fx=2cos5x+3sin4x The period is 2π as f2π+x=fx The fourier polynomial of degree n is:…

Q: Use Taylor's polynomial of degree 2 of the function f(x) = tan 1(x+1) + x² %3D about c = - 1 to…

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Q: Compute the Fourier Transform of the following function (3 , –n < x < o (1 , 0<x< TI f(x) =

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Q: Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|1 ƒ (x) = = { 1 + 0 is ƒ…

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Q: (ex, if 0 a 3 Represent the function f(x) = { as Fourier cosine integral.

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Q: Find Fourierexpansion of the Punction fcx) = x2 XE [-T, TT] then deduce thetn = | 2' (572 (7)2t. (2)…

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

Q: From the definition, derive a general expression for the form of the DTFT of functions of the form…

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Q: 6. Find the Taylor polynomial T,(x) for the function f(x)= cosx at a="/ it to estimate cos(29780)

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Q: Consider the function f(x) = cosa, -, . Construct the Lagrange interpolation polynomial which…

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Q: find the nth Maclaurin polynomial for the function

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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: Show that the Fourier sine transform of the function 0 < x≤1 {:- 1-x 1 ≤ x ≤ 2 2≤x is given by 2 sin…

A: I think the given answer is not correct.

Q: The non-periodic function f(x) is defined by f(x) = e-l=l. Obtain the Fourier transform of f(x).

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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: skla 8. What is the value of Fourier discrete function & [k] at k = 1?

A: To determine: The value of the Fourier discrete function δk at k=1.

Q: (-1)"–1 n2 2 1

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Q: 8. Find the 6th order Fourier approximation of the function that is periodic and f(x) = x, -2<x <2

A: Given function is fx=x ,   -2≤x≤2 Compare the interval  -2≤x≤2 with -L≤x≤L, we get L=2…

Q: (1) Let f(x) = 1,x > 0 with domf= R4+. Find the conjugate of function f(x). %3D

A: given fx=1x , x&gt;0 with domf=R++ claim- find the conjugate of function fx

Q: Let p(x) be a polynomial function of degree n with simple roots r1,..., xn. Show that ) p"(x;) = 0.…

A: Let Pn be a given statement for all natural numbers n. If  i. P1 is true ii. Pk+1 is true whenever…