On the uniform ADC bit precision and clip level computation for a Gaussian signal

The problem of computing the required bit precision of analog-to-digital converters is revisited with emphasis on Gaussian signals. We present two methods of analysis. The first method fixes the probability of overload and sets the dynamic range of the quantizer to accommodate the worst-case signal-to-quantization noise ratio (SQNR). The second method sets the clipping level of the quantizer to meet a desired overload distortion level, using knowledge of the input probability density function. New closed-form expressions relating the distortion-minimizing clip level of the uniform quantizer and the input bit rate are derived and shown to give remarkably close results to the optimum ones obtained using numerical iterative procedures devised elsewhere.