A perturbation theory on statistical quantization effects in fixed-point DSP with non-stationary inputs

A quantitative characterization of statistical quantization effects in a discrete-time digital system is derived as a function of fixed-point data types. The analysis is based on a perturbation theory approach which assumes the quantization noise is a small deviation from the ideal characteristics and that the system does not contain decision-error propagation. The theory works for both linear and nonlinear digital systems with either stationary or nonstationary inputs. The approach is applied to an LMS adaptive filter in both the transient and steady state periods.