 
Summary: On the Uniform ADC Bit Precision and Clip Level
Computation for a Gaussian Signal
Naofal AlDhahir \Lambda , Member, IEEE, and John M. Cioffi, Senior Member, IEEE
Stanford University, Stanford CA 94305 y
Abstract
The problem of computing the required bit precision of analogtodigital converters is revisited with
emphasis on Gaussian signals. We present two methods of analysis. The first method fixes the proba
bility of overload and sets the dynamic range of the quantizer to accommodate the worstcase signalto
quantization noise ratio. 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 closedform ex
pressions relating the distortionminimizing 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 in [6, 9, 10].
I. Introduction
Amplitude quantization refers to the transformation of an analog sample that can take a continuum
of values into one that can only assume a finite set of levels. Inherent in the quantization process is the
introduction of quantization noise that has two components: granular noise and overload distortion due
to quantization errors that arise when the input signal amplitude lies within or outside the maximum
input range of the quantizer, respectively.
In this correspondence, the focus on Gaussian input signals is motivated by our interest in multi
