Can compressed sensing beat the Nyquist sampling rate?

Abstract: Data saving capability of "Compressed sensing (sampling)" in signal discretization is disputed and found to be far below the theoretical upper bound defined by the signal sparsity. On a simple and intuitive example, it is demonstrated that, in a realistic scenario for signals that are believed to be sparse, one can achieve a substantially larger saving than compressing sensing can. It is also shown that frequent assertions in the literature that "Compressed sensing" can beat the Nyquist sampling approach are misleading substitution of terms and are rooted in misinterpretation of the sampling theory.