Suppose you want to find a reasonable sampling period T s for the non-causal exponential x(t)= e

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Suppose you want to find a reasonable sampling period Ts for the non-causal exponential x(t)= e−|t|.

(a) Find the Fourier transform of x(t), and plot |X(Ω)|. Is x(t) band-limited? Use the symbolic function fourier to find the Fourier transform.

(b) Find a frequency ­Ω0 so that 99% of the energy of the signal is in –­Ωo ≤ Ω ­≤­ Ωo.

(c) If we let Ωs = 2π/Ts = 5Ω0 what would be Ts?

(d) Determine the magnitude and bandwidth of an anti-aliasing filter that would change the original signal into the band-limited signal with 99% of the signal energy.

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