How can I make the mean of samples be approximately equal to the mean of actual continuous signal?

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Suppose there is signal f(t) that is continuous and periodic. It is known that this f is T-periodic. (but it's not necessarily a single cosine f(t).( I'd like to make the mean of samples be approximately equal to the man of actual continuous f(t).

Is the use of nyquist sampling rate mandatory in such a case? Or is there a better way to do this?