Verify the pulse width-bandwidth relationship of Equation (2.234) for the following signals. Sketch each signal and its

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Verify the pulse width-bandwidth relationship of Equation (2.234) for the following signals. Sketch each signal and its spectrum.

(a) x(t) = A exp (-t2 / 2τ2) (Gaussian pulse) 

(b) x(t) = A exp (-α |t|), (Gaussian pulse) α > 0 (double-sided exponential)

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