Show that the Fourier transform of sin(a.r) is given by ni [8(2rk + a) – 8(2rk – a)], where a > 0 and k is the Fourier transform variable. The scaling property of the Dirac d might be useful: 8(ax) = 8(x)/|a|.

Q: What is the Fourier transform of the function 4 cos(5t) on the interval [-x, a]| Select one: O a. 4…

A: Here we have to find the Fourier transformation of the function x(t) = 4 cos (5t) Using the formula:…

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

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Q: In the case where a = -T and b = T, compute (sin px, sin qx), (sin px, cos qx), and (cos px, cos…

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Q: 5 sin [ -5TT X<ST %3D otherwise

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Q: If f(x) has the Fourier transform F(p), then f(x) cos ax has the Fourier transform [F(p-a) + F(p +…

A: If Fourier transform of f(x) is F(p), then we have to prove that the Fourier transform of f(x)…

Q: Q8 Find the Fourier transforms of: sin* - pn Sx< pn f(x) otherwise

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Q: then prove that i) F, [ƒ (x) cos ax] = [f, (p + a) +f, (p a)] 1 ii) F.[f(x) sin ax] 2 [f. (p + a) –…

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Q: e> and deduce that Find Fourier sine transform of- ar e bx e | sin px dx = Tan2 - Tan a

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Q: Find the Fourier transform of 4x if 121 <a f(x) - o if 1x129

A: To find the Fourier transform of the function  fx=4x,  if x&lt;a0,    if x&gt;a

Q: 3. Find the transformation fourier function from the following exponential function: fk) = e " jika…

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Q: Find the complex fourier Intergral Representationn of 0, x 0

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Q: Find the finite difference formula for the second derivative at point x=x; with points X₁, Xi+1,…

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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: Show that d(w) - = [6(w− 1) + 6(w+1)] is the Fourier transform of cos(t). Show that d(w) = −ix[8(w −…

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Q: 16. Let V be the set of vectors (x,y, z) E R³ such that r(y² + z²) = 0. Is V a subspace of R³? 17.…

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Q: Find the Fourier Cosine Transform of the function 031.png ... f(x)= (ae¯mx + hex} if x>0 -nx if a =…

A: Please check step 2 and 3 for the solution.

Q: for 0sxs 10 for r> 10 sin(x) for 0srs2x for x> 2x

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Q: (еxp(-ах) when |x| 1 1

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Q: Suppose a 3rd order constant coefficient ODE has a characteristic equation that had 3 distinct…

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Q: Problem 2. For the function defined by if -22x20 0<x<2 52 - 2 f(x) = 2x+2 sketch the 4- Period…

A: As per the question we are given a piecewise defined function f(x)  with period 4 and we have to…

Q: (k) f(x) =X[a.b](x) eiaz,

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Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

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

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Q: the Fourier transform of a continuous time signal x(t) is X(ja), then, the Fou ansform of the signal…

A: Given, Fourier transform of a continuous-time signal                                   x(t)  ↔…

Q: Prove that Fourier cosine transform of f(x) = cos(x), 0<x<3 is: 1/27 (³ sin 3(p-1), sin 3(p+1) p-1 +…

A: Introduction: A Fourier remodel (FT) is a mathematical remodel that decomposes features relying on…

Q: 7)Use Taylor theorem to estimate cos(0.23) with Jerror|< 10-2

A: Here we are to estimate cosx at x=0.23=23100 with error≤10-2,using Taylor theorem i.e, using Taylor…

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: approximate the value of cos (1/2) (sixth degree Maclaurin polynomial)

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Q: Find Phe Fourier tiansform X, In whot sense exist ? %3D does it

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Q: Show the Complex Fourier Integral Transform (Fourier transform) of the function defined below f(t) =…

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Q: Find fourier cosine transform of for 0 1

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Q: XP+2ap +2a') ple 23: Find the inverse Fourier sine transform f(x) of F, (P- ap

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

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Q: Calculate the complex exponential Fourier coefficients for the signal shown below Note:- the…

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Q: Let. a 3 = (-) = -(1) - P = ( ) 5 and a) Find Fourier Coefficient of b with respect to a . b) Find…

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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: 2) Given: f(x) = (x-1) (x+ 1) was transformed to (x) = (x- 1)(x+ 1)-1. How many roots would the…

A: f(x)=(x-1)2(x+1)2 was transformed to f(x)=(x-1)2(x+1)2-1.