ASN7 - Sampled half of signal

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Rule of thumb for sampling is sample slightly greater than the signal. Suppose you sampled only half of the signal can you do something to recover the whole original signal again?

Lets imagine that from our sampling we split the positive and the negative part of the signal. So now we have the negative half repeated on the negative axis and the positive half all along the positive axis.

the trick now is to re-sample at a frequency that will place the negative and positive half side by side. When found that frequency use it sample again. After doing this you should have a number of copies of the original signal. To get just one apply a band pass filter.