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The paper is based upon the statistical theory of signals. It is shown that the variation of the clipped Gaussian noise spectrum is 5 percent, while the normalized cross-correlation function is 0.80; the results are extended to more general cases. A property of the conditional mean value of speech signals is derived. A typical value of the normalized intelligibility of clipped speech in the presence of noise is 0.70 for S/N = 3 dB; assuming the ear is a clipper, theoretical results are well in agreement. The existence of an intelligibility threshold is shown. The need for information on the envelope (or dynamics) of the speech wave to meet the requirement of naturalness is underlined.