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24. The following Fourier pair for the Lorentzian/Cauchy pulse was discussed in class: f(t)-_a (21) where a > 0 is a measure of the width of the time signal. The domains of f (t) and F(w) are -oo < t < oo and-oo <ω<00, respectively. (a) Showing all work, determine the time signal g (t) that has the following Fourier transform, where to is a given constant: G(w) = cos (oto ) e-alco! (b) Showing all work, determine the time signal g (t) that has the following Fourier transform, where ω0 is a given constant: + e 2

Pleaase answer all parts with neat and precise work. show all steps. Please

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