Accurate Sine-Wave Amplitude Measurements Using Nonlinearly Quantized Data

TL;DR

This paper introduces a new amplitude estimation method for sine waves from quantized data that reduces bias and is robust to uncertainties, outperforming traditional least squares estimators in practical measurement scenarios.

Contribution

It proposes a novel amplitude estimation technique that handles non-uniform quantization and phase distribution, improving accuracy over standard methods.

Findings

Reduces bias in amplitude estimation from quantized sine waves.

Robust against small uncertainties in quantizer transition levels.

Effective with non-uniform quantizers and unknown phase distributions.

Abstract

The estimation of the amplitude of a sine wave from the sequence of its quantized samples is a typical problem in instrumentation and measurement. A standard approach for its solution makes use of a least squares estimator (LSE) that, however, does not perform optimally in the presence of quantization errors. In fact, if the quantization error cannot be modeled as an additive noise source, as it often happens in practice, the LSE returns biased estimates. In this paper, we consider the estimation of the amplitude of a noisy sine wave after quantization. The proposed technique is based on a uniform distribution of signal phases and it does not require that the quantizer has equally spaced transition levels. The experimental results show that this technique removes the estimation bias associated with the usage of the LSE and that it is sufficiently robust with respect to small uncertainties in the known values of transition levels.