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: If the function of is odd function (i.e. f(-x) = - f cx)) then, the Fourier transform of f(x) is…

A: Introduction: The Fourier Transform may be used to deal with preliminary boundary cost problems at…

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: 5 sin [ -5TT X<ST %3D 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: Q: The Fourier representation of a function f(x): f(x) = {-10 V, 10 V, ーTくX x > 0 40 sinx sin3x…

A: Given f(x) = -10v.  When -π &lt; x &lt; 0              = 10v when 0 &lt; x &lt; π.   Graph of this…

Q: f(t) = {, - 2 2 -2

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Q: 2) Find the Fourier transforms of: a) b) f(x) = cos(ax), where a > 0. f(x) = x² cos(ax) + x sin(ax),…

A: Since the given problem has multiple sub parts, as per our company guidelines we will solve only the…

Q: Etample T4 Find the inverse finite cosine transform f (x) if (2nn cos 3 where 0<x < 4. F(n) = (2n +…

A: Inverse finite cosine transform

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

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Q: Show that the Fourier transform of f(t) defined by: -3, -a < t < 0 3, f (t) = 0 <t<a Elsewhere where…

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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: (b) Using the Fourier integral formula , show that cos Tw -sin xwdw = {2 if 0n

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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: 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: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…

A: We start with the time-domain signals and their Fourier transforms:Now, the convolution in the time…

Q: The Fourier transform of the function f(t) = 2e-2t cosh 2t u(t)is: 2 4 A- πδ (ω) B- πδ(ω )+ j2w+w?’…

A: We have to use formula for Fourier Transform.

Q: 4. Determine the Fourier transform of the given function: 1 (t) = {2t - t, 2t - 1, 0 < t < 1 0<t<2…

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Q: ii) using the Fourier Transforms, Calculate dx. Jo (4x*)(9+x*)'

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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 Fourier coefficients

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Q: |x] 1 (a) Find the Fourier transform of S(x) = x CoS X - sin dx. (b) Evaluate Jo COS a cos a (а) 2у…

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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: Suppose the function f: R→ R has Fourier transform 1 f(p) = e-p². 1+ 4π²p² i. What is the Fourier…

A: As per the question we are given the Fourier transform of a function f(x) as f̂(p) From that we have…

Q: Show that the finite sine transform of , 0 < x < n is (- 1y*'- p

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Q: Please show all solution with explanation. thanks

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Q: az"¹)]sin(a @)-¹ + a² az-1)2]sin(a w)₂-¹ + a² az-1)³]sin(a @)²-¹ + a² -(az-1)³]sin

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Q: Q1) using Fourier transform find x(t) below x(t) = [e-3tu(t) * e-6*u(t)] dt

A: Solution is given below

Q: Let us assume that given function f can be represented on the interval [-T,7] as a finite linear…

A: `We are given the Finite Fourier series as follows:…

Q: Let f(x) = xsin(x), −â < x < π, then a) Determine the Fourier Transform of f(x) b) Find 8 (−1)” n² -…

A: Introduction: The Fourier transform is a mathematical operation that decomposes a function of time…

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: (-1)"–1 n2 2 1

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