Theorems on power, mean and RMS values of uniformly sampled periodic signals

It is shown that previously published theorems on uniform sampling of signals need modification. Modified theorems are stated and proved. General theorems for exact power evaluation and for the minimum number of samples are stated and proved. A simplified version of the latter theorem, which is useful in practical situations, is restated. Finally, conditions for equal mean and RMS values of sampled and unsampled sinusoidal signals are stated in the form of a theorem followed by a proof.