Correlation function of quantized sine wave plus Gaussian noise

The output correlation function is derived for an -step, symmetric amplitude quantizer when the input is the sum of a sine wave and stationary, zero mean, Gaussian noise. The derivation, which follows the transform method of Rice, Bennett, and Middleton, is perfectly general in that there are no restrictions on the quantizer characteristic or the signal or noise powers. Results of previous studies are restricted to quantizers with uniform steps or to cases in which the rms amplitude of the input is small compared to the amplitude range covered by the quantizer. For low signal-to-noise ratios, approximations can be made which greatly simplify the calculations. These approximations are described, and graphical results are presented for two, three, and four bit linear quantizers when the input noise spectrum is rectangular narrow-band and the SNR is small.