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sampling theory, how to recover amplitude?

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shanmei

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Any time domain signal is composed of some sinusoidal signals. Each sinusoidal signal with frequency Fin can be recovered by the sampling frequency at least twice of Fin. I know that for the sinusoidal signals, two sampling points can alreay confirm this sinusoidal signal, but how it can recoverd the amplitude??

For example, if the sample points are at A and B, the signal time domain information can be confirmed, but how do we know its sinusoidal amplitude? Thanks.
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Obviously, as your diagram shows, you need to sample faster than 2f. Applying that sampled signal to a sinc filter will reconstruct the signal.
 
Consider that the Nyquist criterion requires Fin < fs/2 rather than Fin <= fs/2. Your example shows that for very small differences to fs/2, it takes nearly infinite time to recover the amplitude.
 
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