Analytical Derivation of Quantization Error in Threshold Level Quantizers Using Bipolar PFM

TL;DR

This paper presents an analytical approach to understanding the spectral properties of quantization noise by modeling uniform quantization as bipolar pulse frequency modulation, offering insights into ADC performance.

Contribution

It establishes the equivalence between uniform quantizers and bipolar pulse frequency modulation, providing an intuitive spectral analysis method for quantization noise.

Findings

Spectral structure of quantization noise can be derived using pulse frequency modulation.

The model accurately estimates performance of level crossing ADCs with zero-order-hold interpolators.

Provides a new analytical framework complementing statistical descriptions.

Abstract

Uniform quantization is a topic that has been extensively studied. However and although an analytical description of quantization noise has been proposed, most descriptions of the spectral properties of quantization error resort to statistical descriptions. In this paper, we show how the spectrum of a quantized signal can be expressed using pulse frequency modulation. We first establish the equivalence of a uniform quantizer with a system based on the bipolar pulse frequency modulation and we define afterwards the Fourier transform of the quantized signal using pulse frequency modulation properties. This model brings a more intuitive understanding of the spectral structure of quantization noise and complements prior research in the topic. The results of the paper can be directly applied to level crossing ADCs with zero-order-hold interpolators, giving an accurate estimation of their performance.