Finite limiting effects for a band-limited Gaussian random process with applications to A/D conversion

The theory of finite limiting effects for a band-limited Gaussian random process is reviewed and a mathematical expression for the asymptotic distortion spectrum is derived which is accurate for frequencies outside of the original bandwidth. An expression is also derived for the total distortion power which is shown to be useful for estimating the aliased distortion spectrum when sampling is employed to form a discrete-time signal. An important application of these results is in A/D conversion, where the input signal is implicitly limited by the largest quantization level. Curves are given for the overall signal-to-distortion-plus-quantization-noise ratio (SDQR) as a function of normalized input level and number of bits carried, and show that the maximum SDQR is realized over a narrow range of input levels which is centered at about -12 dB relative to full-scale for an 8-bit A/D.