<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, the complete statistical characterization of the amplitude spectrum at the output of a multiple-input ADC-based measurement system is derived under the assumption of input channels with different noise levels. In practical applications the input channels correspond to the spatial components of a vector field (e.g., magnetic/electric field). Each output spectral line represents the amplitude of the vector field at a specific frequency. Such amplitude is a random variable depending on the noise levels (internal and external noise) of the input channels. Closed form analytical solution for the probability density function of the vector field amplitude is not available in the mathematical literature under the hypothesis of different noise levels. Therefore, an analytical expression for the probability density function is derived on the basis of a Laguerre series expansion. The impact of the kind of time window, the sampling frequency, and the number of samples is clearly derived and put into evidence. Approximate analytical expressions for the mean value and the variance of the vector field amplitude are also provided. Analytical results are validated by means of numerical simulations.</p></abstract>

In this paper, the complete statistical characterization of the amplitude spectrum at the output of a multiple-input ADC-based measurement system is derived under the assumption of input channels with different noise levels. In practical applications the input channels correspond to the spatial components of a vector field (e.g., magnetic/electric field). Each output spectral line represents the amplitude of the vector field at a specific frequency. Such amplitude is a random variable depending on the noise levels (internal and external noise) of the input channels. Closed form analytical solution for the probability density function of the vector field amplitude is not available in the mathematical literature under the hypothesis of different noise levels. Therefore, an analytical expression for the probability density function is derived on the basis of a Laguerre series expansion. The impact of the kind of time window, the sampling frequency, and the number of samples is clearly derived and put into evidence. Approximate analytical expressions for the mean value and the variance of the vector field amplitude are also provided. Analytical results are validated by means of numerical simulations.

Noise Propagation in Multiple-Input ADC-Based Measurement Systems

Department of Electronics, Information and Bioengineering, Politecnico di Milano, piazza Leonardo da Vinci, 32, 20133, Milan, Italy

Measurement Science Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Noise Propagation in Multiple-Input ADC-Based Measurement Systems"}

In this paper, the complete statistical characterization of the amplitude spectrum at the output of a multiple-input ADC-based measurement system is derived...

Noise Propagation in Multiple-Input ADC-Based Measurement Systems

Published Online: Dec 15, 2014

Page range: 302 - 307

Received: Apr 14, 2014

Accepted: Oct 24, 2014

DOI: https://doi.org/10.2478/msr-2014-0041

Keywords
Statistics, noise, analog-to-digital conversion, discrete Fourier transform, frequency domain analysis

© 2014 Diego Bellan

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Noise Propagation in Multiple-Input ADC-Based Measurement Systems

Published Online: Dec 15, 2014

Page range: 302 - 307

Received: Apr 14, 2014

Accepted: Oct 24, 2014

DOI: https://doi.org/10.2478/msr-2014-0041

KeywordsStatistics, noise, analog-to-digital conversion, discrete Fourier transform, frequency domain analysis

© 2014 Diego Bellan

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Statistics, noise, analog-to-digital conversion, discrete Fourier transform, frequency domain analysis