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 + √√27 0

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

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Q: Find the Fourier transform of S (x) =!-\,| sin x dx Hence evaluate

A: Given,    f(x)= 1-x, x≤10        , x&gt;1

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

A: We have to solve given problem:

Q: Find f(x) = f a-1x1 0 the Fourier a-1x1, Hence prove transform Ixl <a , Ixla that 1 (sin t t 0 2 of…

A: Given f(x)=a-x,x&lt;a i.e., -a&lt;x&lt;a                   =0,         x&gt;a i.e., x&gt;a, x&lt;-a…

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: Find sine transform of e-[165]t/t

A: The Fourier sine transform is defined as                                  Fsfx = Fss = ∫0∞fx sinsx…

Q: Find the inverse Fourier transform of the function 10 sin(3) w+T

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Q: Find fourier cosine transform of for 0 1

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Q: Determine the inverse Z-transform of X(z) Select one: akt xk = = (-2j) sin( 2 (2a)k-1 sin (47) 2 xk…

A: Inverse Z transform of the function

Q: What is the Fourier transform of: f(t)=sgn(t) e? Your answer should be expressed as a function of w…

A: Given a function ft=7i2sgnte−8t Explanation ft=7i2e−8t       for t&gt;0 ; t&gt;0 sgnt=1−7i2e8t…

Q: 1) Find the Fourier Sine transform of the function f(x) = re %3D

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Q: f(x)= 2+ Show that fe L²(R) and find the L²-norm of the Fourier transform of

A: Answer given below.

Q: A)) Q1/ Find Fourier Sine Integral presentation of the function: f(x) = xe-* , x>0

A: The given function is: f(x)=xe-x ,      x&gt;0

Q: Find the Fourier transform for f (x) xe c > 0

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Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5) (320° – sin 20 + jln5)*

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Q: Σ 4 NITX (пл)з (1- сos(пп)) sin. L f(x) = n=1 8

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Q: Find the inverse transform of X(z) = -3z 2z² - 5z +2 given that the ROC includes the unit circle.

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Q: a) Find the Fourier Transform of f(x) = = √2πx³ex, 0<x< 6

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

Q: Determine the Fourier transform of f if f(x)=e* for x> 0 and f(x)=sinh2x when x< 0.

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Q: What is the Fourier Transform of sinc(2*x) ? Please show your work. I'm so confused

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Q: Prove that the Fourier sine and cosine transforms are linear.

A: The proof that Fourier sine and cosine transforms are linear is shown below.