If the function of is odd function (i.e. f(-x) = - f cx)) then, the Fourier transform of f(x) is called Fourier sine transform and denoted by Fs { fcx)}, which is defined by: @ Fs (P) = √√ = √²f α) simpx dx = Fs [f(x)} © £ ²x1 = F5¹ { Fs (²) { = √ = {Fs (p) sin p x dp

Q: Find inverse Z-transform 1+- X(z) = (1 - -)*

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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: 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: Show that the Fourier transform of f (x)= e*/2 is e

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Q: Prove that f(x)=log(x)-x^2 +1 has exactly two roots namely x=1 and x=0.45

A: Function: f(x)=log(x)-x2+1 If it has two roots x=1 and x=0.45 then f(1)=0 and f(0.45)=0.

Q: Find the Fourier transform F(e-az) of f(x) = e-a if x > 0 and f(x) = 0 if x 0.

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Q: Which expression to (3 + i)(1 - i)? Note i √-1. O4+i O 4 O2 - 2i O4 - 2i is equivalent

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Q: 1. Let F : L² (R¹) → L²(R¹) be the Fourier transform. That is: 1 F(f) = = √e-i(+1) e-i(x,x) f(x) dx.…

A: Problem is solved using concept of Fourier Transform.

Q: Find out a real-life problem, which can be solved using the Fourier Transform Techniques. Also, give…

A: A Fourier series is a way of representing a periodic function as a (possibly infinite) sum of sine…

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: Determine whether or not the given function is one-to-one and, if 7 so, find the inverse:…

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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: Determine The Fourier transform of the following function (2 |t| t/2 f(t) =

A: Fourier transformation of the function f(t): Fourier transformation of the function f(t) is given…

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: F{6f"(x) – 2f' (x) + 7f(x)} =

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Q: Suppose f is an invertible function and f^-1 is its inverse. Explain how we can use the chain rule…

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Q: 9) Find fxyy for the following function хуу f(x, y) = 4x³y² - 3x²y² + 2x³y-ex²

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

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Q: Obtain the inverse Fourier transform of sen(4(w+2)) (w+2)(3-((w+2)) F(w) =

A: The given function is Simplify the expressions using partial fractionsMultiply both sides of the…

Q: 4.35 (Inverse Transforms) For each X(2), find the signal rn] for each valid ROC. 322 (a) X(2) = +…

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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: Could the limit as xà1 of f(x)=(x+sinx)/(1+x+cosx) be found simply by substituting 1 into the…

A: Given function f(x)=(x+ sin (x))/(1+x+ cos (x)) Now we will evaluate limit of f(X) as X tends to 1…

Q: Find f(x) if its Sine Transform is Hence find F, ().

A: Given that f(x)=e-axx The fourier sine transform is  Fs=∫0∞f(x)sinsxdx=∫0∞e-axxsinsxdx…

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: 0.x 1

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Q: Find the Inverse Z-transform for X(z)=(z+1)/((z-1)(z-2)(z-3))

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