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Q1:

Find the Fourier transform of the half cosine pulse as shown below :

A 0.5 {sin c [0.25(f - 1)] + sin c [2.5(f + 1)]}

B 0.5 {sin c [0.5(f - 1)] + sin c [0.5(f + 1)]}

C 0.25 {sin c [0.25(f - 1)] + sin c [0.25 (f - 1)]}

D 0.25 {sin c [0.5(f - 1)] + sin c [0.5(f - 1)]}

ANS:B - 0.5 {sin c [0.5(f - 1)] + sin c [0.5(f + 1)]}

The given signal can be expressed as multiplication of x1(t) and x2(t) as shown below. where A = 2, T/2 = 0.25 => T = 0.5 ∴ x(t) = x1(t) x x2(t) => X(f) = X1(f) * X2(f) Now X1(f) = [δ(f - f0) + δ(f + f0)] = [sin c [T(f - f0)] + sin c[T(f + f0)]] Now, A = 2, T = 0.5 and f0 = = 1 => X(f) = 0.5[sin c (0.5(f - 1)) + sin c (0.5(f + 1))].



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