1. bookVolume 14 (2014): Issue 6 (December 2014)
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
access type Open Access

Noise Propagation in Multiple-Input ADC-Based Measurement Systems

Published Online: 15 Dec 2014
Volume & Issue: Volume 14 (2014) - Issue 6 (December 2014)
Page range: 302 - 307
Received: 14 Apr 2014
Accepted: 24 Oct 2014
Journal Details
License
Format
Journal
eISSN
1335-8871
First Published
07 Mar 2008
Publication timeframe
6 times per year
Languages
English
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.

Keywords

[1] Bellan, D., Gaggelli, A., Maradei, F., Mariscotti, A., Pignari, S.A. (2004). Time-domain measurement and spectral analysis of nonstationary low-frequency magnetic-field emissions on board of rolling stock. IEEE Transactions on Electromagnetic Compatibility, 46 (1), 12-23.10.1109/TEMC.2004.823607Search in Google Scholar

[2] Krug, F., Mueller, D., Russer, P. (2004). Signal processing strategies with the TDEMI measurement system. IEEE Transactions on Instrumentation and Measurement, 53 (5), 1402-1408.10.1109/TIM.2004.834090Search in Google Scholar

[3] Bellan, D., Gaggelli, A., Pignari, S.A. (2009). Noise effects in time-domain systems involving three-axial field probes for the measurement of nonstationary radiated emissions. IEEE Transactions on Electromagnetic Compatibility, 51 (2), 192-203.10.1109/TEMC.2009.2016107Search in Google Scholar

[4] Kay, S.M. (1988). Modern Spectral Estimation: Theory & Applications. Prentice-Hall.Search in Google Scholar

[5] Schoukens, J., Renneboog, J. (1986). Modeling the noise influence on the Fourier coefficients after a discrete Fourier transform. IEEE Transactions on Instrumentation and Measurement, 35 (3), 278-286.10.1109/TIM.1986.6499210Search in Google Scholar

[6] Jenq, Y. (1988). Measuring harmonic distortion and noise floor of an A/D converter using spectral averaging. IEEE Transactions on Instrumentation and Measurement, 37 (4), 525-528.10.1109/19.9805Search in Google Scholar

[7] Solomon, O.M. (1992). The effects of windowing and quantization error on the amplitude of frequencydomain functions. IEEE Transactions on Instrumentation and Measurement, 41 (6), 932-937.10.1109/19.199437Search in Google Scholar

[8] Kim, Y., Tewfik, A.H., Gowreesunker, B.V. (2012). Multi-channel analog-to-digital conversion using a single-channel quantizer. In 20th European Signal Processing Conference (EUSIPCO). IEEE, 1044- 1048.Search in Google Scholar

[9] Kotz, S., Johnson, N.L., Boyd, D.W. (1967). Series representations of distributions of quadratic forms in normal variables II. Non-central case. Annals of Mathematical Statistics, 38, 838-848.10.1214/aoms/1177698878Search in Google Scholar

[10] Castano-Martinez, A., Lopez-Blazquez, F. (2005). Distribution of a sum of weighted noncentral chisquare variables. Sociedad de Estadistica e Investigacion Operativa, 14 (2), 397-415.Search in Google Scholar

[11] Bellan, D. (2010). Uncertainty effects of unequal noise levels in three-dimensional fields measurement. In International Conference on Signals and Electronic Systems (ICSES). IEEE, 443-446.Search in Google Scholar

[12] Harris, F.J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE, 66 (1), 51-83.10.1109/PROC.1978.10837Search in Google Scholar

[13] Bellan, D. (2013). Detection and estimation of weak sine waves with random offset and additive noise. In 3rd International Conference on Instrumentation, Communication, Information Technology, and Biomedical Engineering (ICICI-BME). IEEE, 156- 161.10.1109/ICICI-BME.2013.6698484Search in Google Scholar

[14] Papoulis, A., Pillai, S.U. (2002). Probability, Random Variables and Stochastic Processes (4th ed.). McGraw- Hill.Search in Google Scholar

[15] Bellan, D., Pignari, S.A. (2008). Noise influence in time-to-frequency transformation of radiated emissions data. In 8th International Symposium on Electromagnetic Compatibility – EMC Europe. IEEE, 731-734.10.1109/EMCEUROPE.2008.4786835Search in Google Scholar

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