Research seminar "Dynamics of the Nonparametric Estimation of the Signal Parameters in the Frequency Domain"

Abstract:
Measurement and estimation of periodic signals parameters, where frequency of the investigated component is the key parameter in estimations, have some restrictions in its practice. Two fundamental principles restrict estimations: the time-frequency uncertainty principle with limited durations of the effective widths of lobes in the time and frequency domains, and the principle of the limited changes of signals - the more smoothly and slowly a function changes, the more rapidly its transformation changes. Both fundamental principles limit the accuracy of parameter estimations and depend on the measurement time. Here it’s meant the relative time to measure a periodic signal or the number of repetitions of the periodicity in it.
The nonparametric approach in parameter's estimations in the frequency domain typically using multi-point interpolated discrete Fourier transformation (DFT) and suitable form of general cosine-sum Rife-Vincent windows. A finite time of measurement is a source of dynamic errors, which are shown as leakage parts of the measurement window spectrum convolved on the spectrum of the measured-sampled signal. Tones of the sampled signal do not generally coincide with the basis set of the periodic components of the DFT. Parameters are calculated from the DFT coefficients around the component peaks by summation to reduce the leakage effects. An estimation of the periodic parameter by the interpolation of the DFT gives the same effect as the reduction of spectrum tails. Side-lobe suppression is at the cost of widening the main lobe and this increases noise contributions. As can be shown, there is a trade-off between a reduction in systematic bias error of the estimations and the noise uncertainty of the estimated results. The number of interpolated points and the used window depend on the mutual positions of the frequency components of the signal, and on the noise level. The optimum for reducing the time of measurement and for reducing systematic errors under non-coherent conditions of sampling real noisy signals could be the estimation with the three cycles window using the three-point interpolation and the Rife-Vincent windows. This can be validated by simulations and experiment results.
 
Biography:
Dušan Agrež received the M.Sc. and Ph.D. degrees in electrical engineering from the Faculty of Electrical and Computer Engineering, University of Ljubljana, in 1990 and 1995, respectively. His working area covers topics on basic electromagnetic measurements, process measurements and automatization of measurement systems. His research interest is mostly in measurement dynamic and parameters estimations. He has published over 98 papers in peer-reviewed journals and conference proceedings and coauthored 2 books. His most cited paper has been approved by 119 citations. Currently, he works as an associate professor at the Faculty of Electrical Engineering, University of Ljubljana. He taught courses in basic measurements, measurement techniques,  measurement instrumentation and systems and measurement dynamics. He was collaborated in many applied projects and transmissions of the knowledge to the industry (firms: METREL Horjul, Elektroelement Izlake, Iskra Ljubljana, …).
He received Milan Vidmar Award for Distinguished Professorship at the Faculty of Electrical Engineering, University of Ljubljana (2008). He received IEEE recognition award as an Outstanding Reviewer for journal IEEE Transactions on Instrumentation and Measurement (2012, 2013) and he is a Senior Member of the IEEE (2010). He is a member of the technical committee IMEKO TC4 - Measurement of Electrical Quantities (2003) and participates in the Technical Committees of several international conferences and symposiums of TC4. He is also a member of the IMEKO Working group on ADC and DAC metrology.