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Metrology and Measurement Systems

The Journal of Committee on Metrology and Scientific Instrumentation of Polish Academy of Sciences

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Volume 22, Issue 1


On the Validity of the Noise Model of Quantization for the Frequency-Domain Amplitude Estimation of Low-Level Sine Waves

Diego Bellan
  • Corresponding author
  • Politecnico di Milano, Department of Electronics, Information and Bioengineering, piazza Leonardo da Vinci 32, 20133 Milan, Italy
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Published Online: 2015-02-20 | DOI: https://doi.org/10.1515/mms-2015-0004


This paper deals with the amplitude estimation in the frequency domain of low-level sine waves, i.e. sine waves spanning a small number of quantization steps of an analog-to-digital converter. This is a quite common condition for high-speed low-resolution converters. A digitized sine wave is transformed into the frequency domain through the discrete Fourier transform. The error in the amplitude estimate is treated as a random variable since the offset and the phase of the sine wave are usually unknown. Therefore, the estimate is characterized by its standard deviation. The proposed model evaluates properly such a standard deviation by treating the quantization with a Fourier series approach. On the other hand, it is shown that the conventional noise model of quantization would lead to a large underestimation of the error standard deviation. The effects of measurement parameters, such as the number of samples and a kind of the time window, are also investigated. Finally, a threshold for the additive noise is provided as the boundary for validity of the two quantization models

Keywords: quantization; amplitude estimation; sine wave; discrete Fourier transform; additive noise


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About the article

Received: 2014-05-18

Accepted: 2014-09-27

Published Online: 2015-02-20

Published in Print: 2015-03-01

Citation Information: Metrology and Measurement Systems, Volume 22, Issue 1, Pages 89–100, ISSN (Online) 2300-1941, DOI: https://doi.org/10.1515/mms-2015-0004.

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© Polish Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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