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Frequency and Damping Estimation Methods - An Overview

Tomasz Zieliński Krzysztof Duda
Metrology and Measurement Systems | 2011 | No 4 | 505-528 | DOI: 10.2478/v10178-011-0051-y
Keywords damped sinusoids frequency estimation damping estimation linear prediction subspace methods interpolated DFT
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Abstract

This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.

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Authors and Affiliations

Tomasz Zieliński
Krzysztof Duda

Fir Filters Compliant with the IEEE Standard for M Class PMU

Krzysztof Duda Tomasz P. Zieliński
Metrology and Measurement Systems | 2016 | vol. 23 | No 4 | 623-636 | DOI: 10.1515/mms-2016-0055
Keywords phasor estimation phasor measurement unit FIR filter cosine window flat-top window
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Abstract

In this paper it is shown that M class PMU (Phasor Measurement Unit) reference model for phasor estimation recommended by the IEEE Standard C37.118.1 with the Amendment 1 is not compliant with the Standard. The reference filter preserves only the limits for TVE (total vector error), and exceeds FE (frequency error) and RFE (rate of frequency error) limits. As a remedy we propose new filters for phasor estimation for M class PMU that are fully compliant with the Standard requirements. The proposed filters are designed: 1) by the window method; 2) as flat-top windows; or as 3) optimal min-max filters. The results for all Standard compliance tests are presented, confirming good performance of the proposed filters. The proposed filters are fixed at the nominal frequency, i.e. frequency tracking and adaptive filter tuning are not required, therefore they are well suited for application in lowcost popular PMUs.
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Authors and Affiliations

Krzysztof Duda
Tomasz P. Zieliński

Impact of Wall Impedance Phase Angle on Indoor Sound Field and Reverberation Parameters Derived from Room Impulse Response

Mirosław Meissner Tomasz G. Zieliński
Archives of Acoustics | 2022 | vol. 47 | No 3 | 343-353 | DOI: 10.24425/aoa.2022.142008
Keywords room acoustics complex wall impedance indoor sound field room impulse response reverberation parameters
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Abstract

Accurate definition of boundary conditions is of crucial importance for room acoustic predictions because the wall impedance phase angle can affect the sound field in rooms and acoustic parameters applied to assess a room reverberation. In this paper, the issue was investigated theoretically using the convolution integral and a modal representation of the room impulse response for complex-valued boundary conditions. Theoretical considerations have been accompanied with numerical simulations carried out for a rectangular room. The case of zero phase angle, which is often assumed in room acoustic simulations, was taken as a reference, and differences in the sound pressure level and decay times were determined in relation to this case. Calculation results have shown that a slight deviation of the phase angle with respect to the phase equal to zero can cause a perceptual difference in the sound pressure level. This effect was found to be due to a change in modal frequencies as a result of an increase or decrease in the phase angle. Simulations have demonstrated that surface distributions of decay times are highly irregular, while a much greater range of the early decay time compared to the reverberation time range indicates that a decay curve is nonlinear. It was also found that a difference between the decay times predicted for the complex impedance and real impedance is especially clearly audible for the largest impedance phase angles because it corresponds approximately to 4 just noticeable differences for the reverberation metrics.
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Authors and Affiliations

Mirosław Meissner
1
Tomasz G. Zieliński
1
  1. Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

Fast one-cycle frequency estimation of a single sinusoid in noise using downsampled linear prediction model

Krzysztof Duda Tomasz P. Zieliński
Metrology and Measurement Systems | 2021 | vol. 28 | No 4 | 661-672 | DOI: 10.24425/mms.2021.137701
Keywords frequency estimation linear prediction Prony method smart DFT
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Abstract

A new solution to the problem of frequency estimation of a single sinusoid embedded in the white Gaussian noise is presented. It exploits, approximately, only one signal cycle, and is based on the well-known 2nd order autoregressive difference equation into which a downsampling is introduced. The proposed method is a generalization of the linear prediction based Prony method for the case of a single undamped sinusoid. It is shown that, thanks to the proposed downsampling in the linear prediction signal model, the overall variance of the least squares solution of frequency estimation is decreased, when compared to the Prony method, and locally it is even close to the Cramér–Rao Lower Bound, which is a significant improvement. The frequency estimation variance of the proposed solution is comparable with, computationally more complex, the Matrix Pencil and the Steiglitz–McBride methods. It is shown that application of the proposed downsampling to the popular smart DFT frequency estimation method also significantly reduces the method variance and makes it even better than the least squares smart DFT. The noise immunity of the proposed solution is achieved simultaneously with the reduction of computational complexity at the cost of narrowing the range of measured frequencies, i.e. a sinusoidal signal must be sufficiently oversampled to apply the proposed downsampling in the autoregressive model. The case of 64 samples per period with downsampling up to 16, i.e. 1/4th of the cycle, is presented in detail, but other sampling scenarios, from 16 to 512 samples per period, are considered as well.
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Bibliography

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[5] Duda, K., & Zielinski, T. P. (2013). Efficacy of the frequency and damping estimation of a real-value sinusoid. IEEE Instrumentation & Measurement Magazine, 16(1), 48–58. https://doi.org/10.1109/ MIM.2013.6495682
[6] Borkowski, J., Kania, D., & Mroczka, J. (2018). Comparison of sine-wave frequency estimation methods in respect of speed and accuracy for a few observed cycles distorted by noise and harmonics. Metrology and Measurement Systems, 25(1), 283–302. https://doi.org/10.24425/119567
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Authors and Affiliations

Krzysztof Duda
1
Tomasz P. Zieliński
2
  1. AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, Department of Measurement and Electronics, al. Mickiewicza 30, 30-059 Kraków, Poland
  2. AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Institute of Telecommunications, al. Mickiewicza 30, 30-059 Kraków, Poland

Acoustic Absorption of a New Class of Alumina Foams with Various High-Porosity Levels

Tomasz G. Zieliński Marek Potoczek Romana E. Śliwa Łukasz J. Nowak
Archives of Acoustics | 2013 | vol. 38 | No 4 | 495-502 | DOI: 10.2478/aoa-2013-0059
Keywords sound absorption porous materials alumina foams
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Abstract

Recently, a new class of ceramic foams with porosity levels up to 90% has been developed as a result of the association of the gelcasting process and aeration of the ceramic suspension. This paper presents and discusses original results advertising sound absorbing capabilities of such foams. The authors man- ufactured three types of alumina foams in order to investigate three porosity levels, namely: 72, 88, and 90%. The microstructure of foams was examined and typical dimensions and average sizes of cells (pores) and cell-linking windows were found for each porosity case. Then, the acoustic absorption coefficient was measured in a wide frequency range for several samples of various thickness cut out from the foams. The results were discussed and compared with the acoustic absorption of typical polyurethane foams proving that the alumina foams with high porosity of 88-90% have excellent sound absorbing properties competitive with the quality of sound absorbing PU foams of higher porosity.
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Authors and Affiliations

Tomasz G. Zieliński
Marek Potoczek
Romana E. Śliwa
Łukasz J. Nowak

Tectonic-climatic interactions during changes of depositional environments in the Carpathian foreland: An example from the Neogene of central Poland

Marek Widera Tomasz Zieliński Lilianna Chomiak Piotr Maciaszek Robert Wachocki Achim Bechtel Barbara Słodkowska Elżbieta Worobiec Grzegorz Worobiec
Acta Geologica Polonica | vol. 71 | No 4 | 519-542 | DOI: 10.24425/agp.2020.134567
Keywords River type Lignite seam Sedimentology Tectonics climate Miocene
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Abstract

Many geological problems have not been convincingly explained so far and are debatable, for instance the origin and changes of the Neogene depositional environments in central Poland. Therefore, these changes have been reconstructed in terms of global to local tectonic and climatic fluctuations. The examined Neogene deposits are divided into a sub-lignite unit (Koźmin Formation), a lignite-bearing unit (Grey Clays Member), and a supra-lignite unit (Wielkopolska Member). The two lithostratigraphic members constitute the Poznań Formation. The results of facies analysis show that the Koźmin Formation was deposited by relatively high-gradient and well-drained braided rivers. Most likely, they encompassed widespread alluvial plains. In the case of the Grey Clays Member, the type of river in close proximity to which the mid-Miocene low-lying mires existed and then were transformed into the first Mid-Miocene Lignite Seam (MPLS-1), has not been resolved. The obtained results confirm the formation of the Wielkopolska Member by low-gradient, but mostly well-drained anastomosing or anastomosing-to-meandering rivers. The depositional evolution of the examined successions depended on tectonic and climatic changes that may be closely related to the mid-Miocene great tectonic remodelling of the Alpine-Carpathian orogen. This resulted in palaeogeographic changes in its foreland in the form of limiting the flow of wet air and water masses from the south and vertical tectonic movements.
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Authors and Affiliations

Marek Widera
1
Tomasz Zieliński
1
Lilianna Chomiak
1
Piotr Maciaszek
2
Robert Wachocki
3
Achim Bechtel
4
Barbara Słodkowska
5
Elżbieta Worobiec
6
Grzegorz Worobiec
6
  1. Adam Mickiewicz University, Institute of Geology, Krygowskiego 12, 61-680 Poznań, Poland
  2. Polish Geological Institute – National Research Institute, Marine Geology Branch, Kościerska 5, 80-328 Gdańsk, Poland
  3. Konin Lignite Mine, 600-lecia 9, 62-540 Kleczew, Poland
  4. Montanuniversitaet Leoben, Austria, Department of Applied Geosciences and Geophysics, Peter-Tunner-Str. 5, A-8700 Leoben, Austria
  5. Polish Geological Institute – National Research Institute, Rakowiecka 4, 00-975 Warszawa, Poland
  6. W. Szafer Institute of Botany, Polish Academy of Sciences, Lubicz 46, 31-512 Kraków, Poland

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