(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let the signal [itex]x(t) = \left(\displaystyle\frac{\sin(50\pi t)}{\pi t}\right)^2[/itex], which we want to sample with sampling frequency [itex]\omega_s = 150\pi[/itex] in order to obtain a signal, [itex]g(t)[/itex] whose Fourier transform is [itex]G(\omega)[/itex]. Determine the maximun value for [itex]\omega_0[/itex] which guarantees that [itex]G(\omega) = 75X(\omega)[/itex] for [itex]\left|\omega\right| \leq{\omega_0}[/itex]

2. Relevant equations

Sampling Nyquist theoreme: [itex]\omega_s > 2B[/itex], where [itex]B[/itex] is the signal band-with.

3. The attempt at a solution

[itex]X(\omega) = FT\{x(t)\}[/itex] is a triangular signal with [itex]B = 100\pi[/itex] and amplitude [itex]X(0) = 25[/itex].

From sampling Nyquist theoreme, [itex]150\pi > 200\pi[/itex] is false, so there is aliasing.

I don't know how to finish the problem.

Thank you.

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# Sampling with aliasing

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