State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms of the following functions: - x| : (i) f(x) = { 1¹7 0 (ii) ƒ(x) = xe¯x²/4 x ≤ 1 : |xc|>1

Q: F-¹ ¹(1+jw) (2+jw)

A: L

Q: Find inverse Fourier transform of F(W) %3D W2-2W+3

A: A complex domain function can be transformed into a real-time function through the inverse Fourier…

Q: press the improper rational transform: 3 4 X(z) = 1+ + + 1 3 ms of a polynomial and a proper…

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Q: Q8 Find the Fourier transform of the following functions: p,-1<x <1 f (x) = 0, otherwise p-x,-1<x <1…

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Q: Write the first 4 terms of the Fourier-Legendre expansion of the following function. Put in the…

A: It is known that the Fourier-Legendre polynomial series for a function fx in the interval -1,1 is…

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: Compute the derivative of each of the following functions in the two ways given. F(x) = (1 + 2x)³ by…

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Q: The Fourier transform of some function f(x) is A(k) 1+46,6, where a is some real number whose…

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

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Q: Q5/ find the Fourier expression of f(x). f(x)=x+x² for _π< x <π -

A: I have done solution step by step in detail....go through the solution

Q: Calculate the fourier transform F (P) following function: f(x) = ¹/2x²(x³ + 3x²-5x) OF # Where F(p1…

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Q: Solve the fourier transform of the following functions: 2ix if-1 < x < 1 otherwise 1. f(x)= = {e²

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Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

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

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Q: Find Fourier transformation of f(x) = (1-x) x<1

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Q: Q1. Find the Fourier of the function in Fig.Q1 f(x) -a a x -a Fig.Q1

A: Q1.The function in Fig.Q1 is a sawtooth wave. The function can be defined as:f(x)=πa​xFourier Series…

Q: B. Find the inverse Z-transform of X(z) Z-1

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Q: f(x)= 0, x 1

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Q: Find the Fourier transform $\tilde{f}(p)$ of the function 4x²e-5¹ for x ≥ 0 for x < 0. f(x) = {…

A: fx=4x2e-5xfor x≥00for x&lt;0

Q: Determine the graph and the Fourier coefficients of the following function: that describe the…

A: Determine the Fourier coefficient of f  f(x)= 0 , -π&lt;=x&lt;=0 .

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

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Q: If the Fourier transform of f(x) is f(k): f(x) x (a) Find the Fourier transform of in terms of f(k).…

A: Given that the Fourier transform of  is .We need to find the Fourier transform of  in terms of .We…

Q: (b) Find the inverse Fourier transform of the following: (11) 1 √w√2π (3+jw)

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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: 0.x 1

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