Quantization optimized with respect to the Haar basis

TL;DR

This paper introduces a deterministic quantization method for discrete-time signals that optimizes low-frequency Haar coefficients, providing high-precision quantization without probabilistic assumptions.

Contribution

It presents a novel deterministic quantization technique optimized for low-frequency Haar coefficients, with error bounds analyzed in Fourier space.

Findings

High-precision quantization of low-frequency components

Deterministic method without probabilistic assumptions

Error bounds established in Fourier domain

Abstract

We propose a method of data quantization of finite discrete-time signals which optimizes the error estimate of low frequency Haar coefficients. We also discuss the error/noise bounds of this quantization in the Fourier space. Our result shows one can quantize any discrete-time analog signal with high precision at low frequencies. Our method is deterministic, and it employs no statistical arguments, nor any probabilistic assumptions.