Use a Fourier transform table and properties of the Fourier transform to find the Fourier transform X of each function x

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Use A Fourier Transform Table And Properties Of The Fourier Transform To Find The Fourier Transform X Of Each Function X 1 (67.37 KiB) Viewed 25 times

Use a Fourier transform table and properties of the Fourier transform to find the Fourier transform X of each function x below. (a) x(t) = cos(t-5); (b) x(t) = e¯jstu(t+2); (c) x(t) = cos(t)u(t); (d) x(t)=6[u(t)-u(1-3)]; (e) x(t) = 1/t; (f) x(t) = t rect(21); (g) x(t) = e-j³t sin(5t - 2); (h) x(t) = cos(5t - 2); (i) x(t) = x₁ * x2(t), where x₁ (t) = e-2¹u(t) and x₂ (t) = te-³tu(t); and (j) x(t) = Σoak 8(t-kT), where a is a complex constant satisfying |a| < 1 and T is a strictly-positive real constant; (Hint: Recall the formula for the sum of an infinite geometric sequence (i.e., (F.3)).)