5.7 Use the properties of the Fourier transform in the following problems. (a) Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal x (t) with a Fourier series 00...

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Extracted text: 5.7 Use the properties of the Fourier transform in the following problems. (a) Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal x (t) with a Fourier series 00 x(t) = 1+(0.5)* cos(k2ot). k=1 (b) Find the Fourier transform of 1 x1(t)= a > 0 12+ a² by considering the properties of the transform. Hint: use the FT of e¬alrl for a > 0. Answer: (b) X1(S2) = (1/a)e¬a\2].