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

arXiv: https://arxiv.org/abs/2602.17471 · HTML: https://mlsanity.com/paper/2602.17471/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 14 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 1 of 1)

- [A Different View of Sigma-Delta Modulators Under the Lens of Pulse Frequency Modulation](https://mlsanity.com/paper/2311.06983/) (2023)

## Abstract (arXiv)

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.