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I'm given the signal $x(t)=\cos(100*\pi*t)+\cos(200*\pi*t)+\sin(500*\pi*t)$ and I need to find the least sampling frequency in order to reconstruct the $x(t)$ signal from the following of it's samples.

Any thoughts?

Leucippus
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Γιώργος Χριστόπουλος
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    the Shannon sampling theorem. https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem – reuns May 30 '16 at 02:08

1 Answers1

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You need a sampling frequency that is at least twice the largest frequency present in your signal. In your case, $$\omega_{max} = 500\pi \implies f_{max}=\frac{\omega_{max}}{2\pi}=250\text{Hz} $$

Which means that,

$$\boxed{f_{sampling} \geq 2f_{max} = 500\text{Hz}}$$

Constantinos Vrohidis
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