User:Gummif/sandbox

At first glance, compressed sensing, because it depends on the sparsity of the signal in question and not its highest frequency, might seem to violate the sampling theorem. This is a misconception, because the sampling theorem guaranties perfect reconstruction given sufficient, not necessary, conditions. A sampling method different from the classical fixed-rate sampling therefore can not "violate" the sampling theorem. Sparse signals with high frequency components can be highly under-sampled using compressed sensing compared to classical fixed-rate sampling.