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: 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: 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: 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: 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: 0.x 1

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