Validity of Widrow’s model for sinusoidal signals

This paper surveys the conditions of validity of Widrow’s model [B. Widrow, Statistical analysis of amplitude quantized sampled data systems, Trans. Am. Inst. Elect. Eng., Part II: Appl. Ind. 79 (January) (1960) 555–569] for quantizing sinusoidal signals in a uniform quantizer. The analysis is developed for a generic sinusoidal input signal. Sripad and Snyder’s formulation [A.B. Sripad, D.L. Snyder, A necessary and sufficient condition for quantization errors to be uniform and white, IEEE Trans. Acoust. Speech Signal Process. ASSP-25 (5) (1977) 442–448] is used to establish a general expression for the probability density function (PDF) of the quantization noise. A new technique to speed up the series convergence is presented and the mean value and the variance of the quatization error of a sinusoidal signal applied to a uniform quantizer are calculated.Applications to particular cases are carried out to support the results obtained.