Find the Fourier transform of f (x) defined by |x| < a 1지 > a f (x) = sin? ax ta and hence prove that x2 2

Q: Compute the Fourier Transform of f(x) = e-ax-

A: Fourier transform of a function fx is defined as  Ffx=∫-∞∞fxeisx dx Gamma function =∫0∞e-x xn-1 dx

Q: Let f(x) (x2 +x), -n<x<n be a periodic function, then the Fourier coefficient az %3D Answer:

A: The Fourier series for the function can be calculated using the formula  fx=A0+∑n=1∞…

Q: Find the Fourier transform 1-x, | x | 1 sin x Cos X CoS x Hence evaluate dx.

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Q: Compute the Fourier transform of the following function: f(x, y) = e-()x-y|+|x+y\)&

A: The given function is, fx,y=e-x-y+x+y The two dimensional Fourier transform is defined by,…

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: Find the Fourier transform of f if (e* jkax > 0 * ikax<0 Note : jika = if

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Q: Find the Fourier transform of (a) f (x) = sin (x²), (b) f (x) = cos (x2)

A: 4. Given that,fx=sinx2andfx=cosx2The Fourier transform of the above functions isdetermined as shown…

Q: Find the inverse Z-transform of x (z) = tanh z

A: The given data is: xz=tanh-1z To find inverse z-transformation of the given data.

Q: The best approximation of f(x) = cos(8 + x) by a Fourier polynomial of degree 1 is

A: The Fourier Polynomial of degree n is Fn(x)=a0 + ∑k=1nakcos(kx) +∑k=1nbksin(kx). Then, the Fourier…

Q: Find Fourier transform for f (t-2)

A: We have to solve given problem:

Q: Find the Fourier cosine transform of f(x) = e-2x + 4e-3x

A: Given, f(x) = e-2x + 4e-3x Find Fourier cosine transform

Q: Compute the fourier transform of f(x) = e -│x│ Sin2πx , sketch f and its fourier transform , x in R

A: Given function is, fx=e-xsin2πx;x∈ℝ. Graph of f(x) is given by,

Q: Find the finite Fourier Cosine Transform of f(x) = 1- in (0, x).

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Q: 1. Use the differentiation and integration properties of Fourier Transform to find a closed form for…

A: We have, xt=0             t&lt;-12t+12     -12≤t≤121                t&gt;12      Apply Fourier…

Q: Find the Fourier approximation with the specified order of the function on the interval [0, 2π].f…

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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: 27. Explain why this function does or does not have a Fourier transform. If it does, compute its…

A: Consider the given function. fx=0,        x&gt;1excosx,x&lt;1 Fourier transformation is defined as.…

Q: f *g =g *f , where (*) is the convolution in Fourier transform. Select one: True False

A: Given: (*) is the convolution in fourier transform. To prove:  f*g=g*f. Proof: It is known that…

Q: Find the Fourier transform of f (x)- 2ix if -1<x< 1 lo f(x) = otherwise

A: The Fourier transform of the function f(x) is defined as ∫-∞∞eikxf(x)dx. The Fourier transfrom…

Q: . Find the Fourier transform of (x if 0<x< a f(x) 0 otherwise

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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: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: b) Find the Fourier sine transform of f(x) = 12π, 0 < x < 6π

A: Fourier coefficients represent the amplitude of each harmonically-related sinusoid present in the…

Q: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

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Q: Q2/ from definition of Fourier transform, show that rect (t-5) is sinc (w/2)e-/2w

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Q: Find the fourier sine transform of a) f(x) = exp(-ar) and deduce sin(sz) -ds = 2+a² -az b) f(x)= re'…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Find the finite Fourier cosine Transform of f(x) = x2 in 0 < x < 4. CoSx Show that J_2(x) = -sinx –…

A: Multiple :  We need to find Fourier cosine transform of  f(x) = x2  in  0 &lt; x &lt; 4. Cosine…

Q: Find the Fourier transform of (x) (13x if|x] 1

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Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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Q: Let ω be the 8th root of unity and the quantum Fourier transform is defined using this ω. Under this…

A: Given: 'ω' be the 8th root of unity  Quantum fourier transform (QFT), under which we have to check…

Q: f(x)= == ¹xcl! Obtain the Fourier transform of

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Q: a) Find Fourier Transform f (x) = |x| > B and Evaluate Sin[2B]Cos[2x] da -8-

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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: a) Find the finite Fourier cosine Transform of f (x) = x² in 0 < x < 4.

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Q: (b) Find the z-transform of f(-÷)` ux given that Z{ux} z-1

A: Z transform of the function

Q: (a) By making appropriate use of Jordan's lemma, find the Fourier transform of T³ f(x) = (x² + 1)²*

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Q: Find the finite cosine transform of f (x) if ƒ (x) = -x+ in (0, t).

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Q: Find the Fourier transform of (а) f (г) %—D еxp (-ах?), () f (») — еxp (-а \x),

A: To find the Fourier transform of the below functions. fx=e−ax2 fx=e−ax

Q: · findd the fourier sine transform of f(x) = 7 A 9x 0<X<9 otherwise

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Q: 1.) Give the Fourier transform of the function f. Sx ha x = [0, 1] f(x) = 0 otherwise.

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Q: nsform of f(t) = et-T sin 2rdr. %3D

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Q: Find the Fourier scries of the function f(x) = |x| for -1 sx< 1. %3D

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Q: 27. Explain why this function does or does not have a Fourier transform. If it does, compute its…

A: The given function: f(x)=0,             |x|&gt;1excosx,   |x|&lt;1 This function have a Fourier…

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

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Q: Find the finite Fourier Cosine Transform of f (x), where 0<x <"/3 when f(x) = (x – n when T/3<x<n°

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Q: Compute the coefficient Fourier a, of the { T - r, 0<r<* 0, f(r) =

A: We have to compute Fourier coefficient an.

Q: Find the Fourier cosine transform of e-x.

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Q: Find the Fourier Transform of - n<x< 0 0 <x < n f(x) = %3D 1- x

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