A Propagation Analysis of Residual Distributions in Pipeline ADCs

This paper presents a propagation analysis of residual distributions in pipeline ADCs. It relies on the observation that the Frobenius-Perron operator which maps the input probability density of a pipeline stage into its output distribution admits a simple representation in the Fourier domain. It performs a decimation operation followed by a sign modulation operation on the Fourier coefficients of the input density. This representation is used to analyze the convergence of residual distributions to a uniform distribution as more stages are traversed. The analysis can also be used to show that quantization residuals become asymptotically independent. For quantization stages with redundant bits it is also shown that the span of the uniform distribution of quantization residuals need not coincide with the full ADC dynamic range.