The Sampling Theorem states that when you have a signal x(t) bandlimited to B Hz, then if you sample the signal at frequency f_s higher than or equal to 2B, then you can use the sample to reconstruct the original signal x(t) uniquely.(adsbygoogle = window.adsbygoogle || []).push({});

Yet, if you consider the simple sinusoidal signal x(t)=sin(2*pi*B*t), which obviously only has one frequency of B Hz, and sample with a frequency f_s=2B at time t=0,1/(2B),2/(2B),3/(2B),4/(2B),...,n/(2B),... then, all you get is a sequence x_sample(0)=x_sample(1)=...=x_sample(n)=sin(n*pi)=0, and you would naturally conclude that x(t)=0. Wouldn't it be a very simple counter-example to the sampling theorem?

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# Counter-example to Nyquist's Sampling Theorem?

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