What if we sampled at semi-random intervals instead? It could prevent the high-frequency signal from looking the same as the low-frequency one.
Since we have full information about the original signal, can we do some not so expensive feature exaction to learn important points like local extremes, assuming the original function is differentiable or locally differentiable (which usually holds in computer graphics?)?
When we heard the constant frequency initially with the low frequency signals, was the constant frequency due to appropriate sampling (i.e. sampled points are actually on the same level) or the limitation of human brain (i.e. we can't really hear subtle differences)?
Similar to the above ideas, is there a reason we can't figure out the frequency and then sample accordingly? For instance, could we predict the first 1% of the signal, figure out how off we are to the actual, and then adjust our sampling rate based on the results?
curious about good ways to avoid or eliminate aliasing if we want o combine high freq with low freq.