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1

Inflation synchronisation strengthening in Europe in post-quantitative easing and post-pandemic high inflation times: consequences for single monetary policy management

Budová Jana, Šuliková Veronika, Siničáková Marianna

Management

|

2023

|

Vol. 27, no. 2

121--148

EN

This paper aims to find out whether the inflation rates of individual European Union (EU) countries are synchronised with those of the EU as a whole and with the euro area (EA). Another objective is to examine the mutual inflation interconnections and its synchronisation across countries. We use the Minimum Spanning Tree (MST) and cross-correlations (C-C). Based on structural break tests, the period is divided into four periods: January 2001 - December 2008, January 2009 - March 2015, April 2015 - July 2021, August 2021 - April 2023. The results showed that the direction of the inflation transmission is not the same across the periods under study. Before the financial and economic crisis, Estonian inflation influenced Lithuanian inflation, which in turn influenced the Latvian one; while after the crisis (but just before the application of the ECB’s quantitative easing) Latvian inflation is already influenced by Bulgarian inflation. Once quantitative easing had already been applied but in times before the ‘high inflation’ period, the inflation in Lithuania has no impact on the Latvian one. During the ‘high inflation’ period, results conclude the impact of Latvian inflation on the Estonian one. We also point out that inflation rates in some states are not always aligned with average inflation in the EU, the EA. Although, MST results showed that inflation is transmitted mainly from the EA average or the EA countries, having a more central position (e.g. Slovakia has generally a more central position than the Czech Republic, Hungary, or Poland). Therefore, countries having common monetary policy are more resistant to external inflation shocks and rather influence the inflation of other countries. Finally, even if inflation rates are synchronised, inflation may be outpaced or lagged by one to several months, which may present policymakers with the question of the appropriate monetary policy stance.

2

Regresja i niepewność linii prostej dla pomiarów obu zmiennych x i y ze wszystkimi korelacjam

Puchalski Jacek, Warsza Zygmunt Lech

Pomiary Automatyka Robotyka

|

2022

|

R. 26, nr 2

47--58

PL

Praca kontynuuje cykl publikacji o szacowaniu metodą regresji liniowej parametrów równania i granic pasma niepewności linii prostej y = ax + b dopasowanej do wyników pomiarów obu współrzędnych punktów badanych. Rozpatrzono przypadek ogólny, gdy współrzędne te mają różne niepewności i występują wszystkie możliwe autokorelacje i korelacje wzajemne. Zastosowano opis równaniami macierzowymi. Wyniki pomiarów współrzędnych przedstawiono jako elementy wektorów w X i Y. Propagację niepewności opisano macierzą kowariancji UZ o czterech macierzach składowych, tj. UX i UY - dla niepewności i autokorelacji zmiennych X i Y oraz UXY i jej transpozycja UTXY - dla korelacji wzajemnych. Podano równanie linii prostej i granice jej pasma niepewności. Otrzymane je dla funkcji parametrów a i b spełniającej tzw. kryterium totalne WTLS, tj. minimum sumy kwadratów odległości punktów od prostej ważonych przez odwrotności niepewności współrzędnych. Przy nieskorelowaniu współrzędnych różnych punktów stosuje się uproszczone kryterium WLS. Kierunki rzutowania punktów wnikają z minimalizacji funkcji opisującej kryterium. W przypadku ogólnym istnieje tylko rozwiązanie numeryczne. Zilustrowano to przykładem. Parametry a i b linii prostej wyznaczono numerycznie z powiększonych fragmentów wykresu funkcji kryterialnej wokół jej minimum. Podano też warunki wymagane dla niepewności i korelacji współrzędnych punktów, które umożliwiają uzyskanie rozwiązania analitycznego i jego przykład.

EN

The work continues the series of publications on the estimation of the parameters of the equation and the limits of the uncertainty band of the straight-line y = ax + b fitted to the measurement results of both coordinates of the tested points with the use of the linear regression method. A general case was considered when these coordinates have different uncertainties and there are all possible autocorrelations and cross-correlations. Description of matrix equations was used. The results of the coordinate measurements are presented as elements of the X and Y vectors. The propagation of their uncertainty was described by the UZ covariance matrix with four component matrices, i.e., UX and UY - for the uncertainties and autocorrelations of X and of Y, and UXY and its transposition UTXY - for the cross-correlations. The equation of a straight line and of the borders of its uncertainty band are given. Obtained them for the function of parameters a and b satisfying the so-called total criterion WTLS, i.e., the minimum sum of squared distances of points from the straight line weighted by the reciprocal of the coordinate uncertainty. When the coordinates of different points are not correlated, the simplified criterion WLS is used. The directions of projecting the points result from the minimization of the function describing the criterion. In the general case, there is only a numerical solution. This is illustrated by an example, in which the parameters a and b of the straight line were determined numerically from the enlarged fragments of the graph of the criterion function around its minimum. The conditions for the uncertainty and correlation of coordinates of points required to obtain an analytical solution and its example are also given.

3

Application of cross-correlation-based transimpedance amplifier in InAs and InAsSb IR detectors noise measurements

Achtenberg Krzysztof, Mikołajczyk Janusz, Bielecki Zbigniew

Opto-Electronics Review

|

2022

|

Vol. 30, No. 2

art. no. e141126

EN

The paper presents noise measurements in low-resistance photodetectors using a crosscorrelation-based transimpedance amplifier. Such measurements usually apply a transimpedance amplifier design to provide a current fluctuation amplification. In the case of low-resistance sources, the measurement system causes additional relevant system noise which can be higher than noise generated in a tested detector. It mainly comes from the equivalent input voltage noise of the transimpedance amplifier. In this work, the unique circuit and a three-step procedure were used to reduce the floor noise, covering the measured infrared detector noise, mainly when operating with no-bias or low-bias voltage. The modified circuit and procedure to measure the noise of unbiased and biased detectors characterized by resistances much lower than 100 Ω were presented. Under low biases, the reference low-resistance resistors tested the measurement system operation and techniques. After the system verification, noise characteristics in low-resistance InAs and InAsSb infrared detectors were also measured.

4

Effects of detection system parameters on cross-correlations between MUAPs generated from parallel and inclined muscle fibres

Messaoudi Noureddine, Bekka Raïs El’hadi, Belkacem Samia

Polish Journal of Medical Physics and Engineering

|

2021

|

Vol. 27, Iss. 1

87--97

EN

The aim of this study was to investigate the effects of inter-electrode distance (IED), electrode radius (ER) and electrodes configurations on cross-correlation coefficient (CC) between motor unit action potentials (MUAPs) generated in a motor unit (MU) of parallel fibres and in a MU of inclined fibres with respect to the detection system. The fibres inclination angle (FIA) varied from 0° to 180° by a step of 5°. Six spatial filters (the longitudinal single differential (LSD), longitudinal double differential (LDD), bi-transversal double differential (BiTDD), normal double differential (NDD), an inverse binomial filter of order two (IB2) and maximum kurtosis filter (MKF)), three values of IED and three values of ER were considered. A cylindrical multilayer volume conductor constituted by bone, muscle, fat and skin layers was used to simulate the MUAPs. The cross-correlation coefficient analysis showed that with the increase of the FIA, the pairs of MUAPs detected by the IB2 system were more correlated than those detected by the five other systems. For each FIA, the findings also showed that the MUAPs pairs detected by BiTDD, NDD, IB2 and MKF systems were more correlated with smaller IEDs than with larger ones, while inverse results were found with the LSD and LDD systems. In addition, the pairs of MUAPs detected by the LDD, BiTDD, IB2 and MKF systems were more correlated with large ERs than with smaller ones. However, inverse results were found with the LSD and NDD systems.

5

Dynamic evaluation on ride comfort of metro vehicle considering structural flexibility

Chen Zhaowei, Zhu Guo

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 4

463--478

EN

Traditional rigid vehicle model cannot reflect structural local vibration and flexible deformation, which may affect the accuracy in evaluating ride comfort of metro vehicle. Aiming at this issue, this paper proposes a research method of flexible dynamic behavior based on flexible multi-body dynamics (FMBD), considering the structural flexibilities of key parts of metro vehicle in detail, to study the ride comfort of metro vehicle. First, finite element models of carbody and frame are established, which are then reduced by substructure theory and Guyan reduction method. On this basis, the flexible vehicle-track coupled dynamic model is established. After investigating the difference between the flexible model and traditional rigid model, the ride comfort of metro vehicle on straight line and curve line is then evaluated subjected to rail random irregularity, short-wave excitation and long-wave excitation, respectively. Finally, correlations of carbody vibrations at different locations are deeply investigated. Results show that carbody accelerations calculated by flexible model are larger than those obtained by rigid model. The sensitive frequency band of human is obviously reflected and calculated by flexible model, indicating that the ride comfort of metro vehicle can be more accurately evaluated with the flexible vehicle model. Flexible modes and local vibrations are obviously reflected in carbody vibrations. Vibration at PR (point on roof) location is largest, and vibration at PC (point on floor center) location is smallest. Ride comfort is very sensitive to long-wave excitation while is not sensitive to short-wave excitation. It is not accurate enough to evaluate ride comfort of metro vehicle only according to vibration at floor center, and more data at different locations should be concerned, especially vibrations at air spring locations.

6

A new approach in reverse time migration for properly imaging complex geological media

Moradpouri Farzad

Acta Geophysica

|

2021

|

Vol. 69, no. 2

529--538

EN

Reverse time migration (RTM) artifacts usually start to appear in large refection angles which include a wide-angle range. On the other hand, the only proposed starting refection angle for RTM artifacts is 60 degrees which is not based on a proven investigation and it seems to be just a suggestion based on trial and error. As an important issue, we determine a predominant starting refection angle (PSRA) for RTM artifacts which enables us to suppress artifacts properly. Therefore, frst we try to open and discuss some issues from a new fundamentally perspective about the number of cross-correlations (NOCC) and its relationship with RTM amplitude and artifacts at refection and nonrefection points. Second, the cross-correlation and its related NOCC at each subsurface position form a new approach to determine PSRA for RTM artifacts. Using NOCC values, the refection angle of 55 degrees was determined as PSAR at which the RTM artifacts often start to appear. Finally, a new imaging condition based on the down- and upgoing wave felds and a new weighting function were proposed to suppress RTM artifacts. The new imaging condition can maintain the desired information and suppress artifacts properly for the angle domain of 55° to 90°. A key point in the suppressing process is the direct relationship between refection angle and artifact production where each refection angle in the domain of 55° to 90° can produce a diferent amount of artifacts. Therefore, the proposed imaging condition is able to designate a suitable weight for each refection angle to properly maintain the desired amplitude and suppress artifacts.

7

A multifaceted analysis of the relationship between daily temperature of river water and air

Graf Renata

Acta Geophysica

|

2019

|

Vol. 67, no. 3

905--920

EN

The aim of the study was to establish the strength and direction of the relationship between daily temperature of river water and air with the use of selected estimation methods. The relationship was assessed for the River Noteć and its tributaries (Western Poland), using the cross-correlation function and Granger causality. The study established cause-and-effect relations for “water–air” and “air–water” directions of influence. It was confirmed that forecasting the pattern of flowing water temperature from changes in air temperature yields better results when done based on data from the previous day. Results of modelling the relationship between data series with the use of the linear and natural cubic splines models confirmed the presence of a nonlinear relation. It was also established that there is a statistically significant correlation of random fluctuations for both temperature series on the same days. This made it possible to confirm the occurrence of short-term connections between water and air temperature. The results can be used to determine the qualities of thermal regimes and to predict temperature of river waters in the conditions of climate change.

8

Fizyczne podstawy metody interferometrii sejsmicznej

Czarny R.

Zeszyty Naukowe Instytutu Gospodarki Surowcami Mineralnymi i Energią PAN

|

2017

|

nr 101

195--202

PL

Interferometria sejsmiczna jest dynamicznie rozwijającą się metodą, której pierwsze zastosowania sięgają początków obecnego stulecia. Aktualnie znajduje coraz szersze zastosowanie w zagadnieniach m.in. obrazowania głębokich struktur ziemi oraz utworów przypowierzchniowych, monitorowania procesów wulkanicznych oraz analizowania wpływu silnych trzęsień ziemi na obiekty budowlane. Metoda ta pozwala na odtworzenie odpowiedzi impulsowej tzw. funkcji Greena ośrodka pomiędzy parą odbiorników na podstawie zarejestrowanych w tym samym czasie sejsmicznych pól falowych na tych odbiornikach. W wyniku odpowiednich operacji matematycznych metoda ta zamienia zarejestrowane na odbiornikach koherentne fale sejsmiczne o nieznanym czasie oraz miejscu ich wzbudzenia na układ tzw. wirtualnych źródeł emitujących sejsmiczne pole falowe z dowolnego odbiornika. W artykule przedstawiono fizyczne uzasadnienie wyników eksperymentu akustyki odwróconego czasu (ang. time-reversed acoustics) według Derode i in. (2003), które jest zarazem wytłumaczeniem metody interferometrii sejsmicznej. Eksperyment laboratoryjny w pierwszym etapie polegał na rejestracji akustycznego pola falowego wyemitowanego na brzegu naczynia wypełnionego cieczą i stalowymi prętami. Następnie rejestracje zostały odwrócone w czasie i wysłane powtórnie do wewnątrz naczynia i odebrany po przeciwnej stronie. Zarejestrowany na końcu sygnał okazał się zbliżony do sygnału wyemitowanego, pomimo przejścia przez ośrodek wielokrotnie rozpraszający. Doświadczenie to uzasadniono wykorzystując technikę korelacji wzajemnej (ang. cross-correlation), zasadę superpozycji pola falowego oraz zasadę wzajemności Rayleigha.

EN

Seismic interferometry is a geophysical method which has been developing very rapidly over the last decade. It has been applied to image deep structures of the Earth as well as near-surface, monitor volcanic processes, geothermal reservoirs within exploitation, rock mass deformation induced by mining, landslides, ground water storage, ice sheet or the impact of strong earthquakes to buildings. The vast majority of these applications use ambient seismic noise as a seismic source. This method involves reconstructing thte impulse response, the socalled Green’s function, between pair of receivers based on the wave field registered by them. Using seismic interferometry with various data processing flows the registered coherent seismic waves by the receivers can be changed to virtual sources which are placed in the receiver locations. In the article, the physical derivation of the time-reversed acoustics experiment which was introduced by Derode et. al. (2003) is presented. This derivation also explains the seismic interferometry method. The laboratory experiment contained two phases. First, an acoustics signal was emitted into the medium with hundreds of scatterers (cube with liquid and rods) and registered on the opposite side of the medium. Then, registrations were reversed and emitted back. Finally, the wave field refocused exactly in the point of initial excitation. Derode et. al. explain these results using the cross-correlation technique, superposition and Rayleigh’s reciprocity principles.

9

Range resolution improvement of range-gated vision system in backscattering hazy environments

Park S.-K., Choi I.-Y., Baik S.-H., Jeong K.-M.

Optica Applicata

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2017

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Vol. 47, nr 4

533--543

EN

A range-gated vision system simultaneously provides two-dimensional and range images because its light intensity contains the reflectance as well as depth information. The range-resolution of the system is usually inversely proportional to the induced backscattering noise. In this paper, a range imaging technique is proposed to precisely measure range information from highly backscattering foggy environments. A windowed center-of-mass position extracted from the peak area of a cross-correlation signal of two signals, a Gaussian window signal in reduced size and a range-gated signal according to distance, is adopted as the range depth. The proposed measuring technique provides more robust and more precise range information than conventional measuring techniques for hazy targets by virtue of the reduction of backscattering bias noise usually induced by airborne particles. The experimental results and the signal processing procedures to acquire precise range information from hazy targets are described in this paper.

10

Comparison of Time Warping Algorithms for Rail Vehicle Velocity Estimation in Low Speed Scenarios

Hensel S., Marinov M. B.

Metrology and Measurement Systems

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2017

|

Vol. 24, nr 1

161--173

EN

Precise measurement of rail vehicle velocities is an essential prerequisite for the implementation of modern train control systems and the improvement of transportation capacity and logistics. Novel eddy current sensor systems make it possible to estimate velocity by using cross-correlation techniques, which show a decline in precision in areas of high accelerations. This is due to signal distortions within the correlation interval. We propose to overcome these problems by employing algorithms from the field of dynamic programming. In this paper we evaluate the application of correlation optimized warping, an enhanced version of dynamic time warping algorithms, and compare it with the classical algorithm for estimating rail vehicle velocities in areas of high accelerations and decelerations.

11

Cross-correlation function in identifying head checking defects of the railway rails

Lesiak P., Sokołowski A., Wlazło M.

Diagnostyka

|

2017

|

Vol. 18, No. 2

65--73

EN

The cross-correlation function has been applied to the study of the similarity of the two functions. One of these functions is known and represents a defect type HC (Head Checking) in the railway rail. The second function is unknown and based on cross-correlation function of both functions specifies the parameters of the similarities. These functions correspond to defects whose images have been determined using laser scatterometry method. FFT method has been used to calculate these functions.

PL

Zastosowano funkcję korelacji wzajemnej do badania podobieństwa dwóch funkcji. Jedną z tych funkcji jest znana i stanowi opis wzorca wady head checking (HC) w szynie kolejowej. Druga funkcja jest nieznana. Na podstawie funkcji korelacji wzajemnej obu tych funkcji, określa się parametry ich podobieństwa. Funkcje te reprezentują obrazy wyznaczone doświadczalnie, metodą skaterometrii laserowej. W obliczeniach wykorzystano szybką transformatę FFT.

12

Różnicowe i złożone metody analizy sygnałów w radioizotopowych pomiarach prędkości fazy rozproszonej w przepływie ciecz-gaz w rurociągu poziomym

Hanus R., Zych M., Petryka L.

Przegląd Elektrotechniczny

|

2015

|

R. 91, nr 4

60--63

PL

W pracy przedstawiono przykład zastosowania absorpcyjnej metody radioizotopowej w badaniach przepływów dwufazowych typu ciecz - gaz w rurociągu poziomym. Zasadniczą część pracy poświęcono przedstawieniu zastosowanych metod analizy sygnałów uzyskiwanych z detektorów scyntylacyjnych. Ponieważ sygnały te są przebiegami stochastycznymi, do ich analizy zastosowano metody statystyczne wykorzystujące średni modułu różnicy amplitud, średni kwadrat różnicy amplitud, funkcję korelacji wzajemnej oraz metody złożone będące połączeniem metod różnicowych i korelacyjnej.

EN

This paper presents an application of the gamma absorption method for two-phase liquid-gas flow evaluation in a horizontal pipeline. For analysis of stochastic signals obtained from the scintillation detectors such methods as the average magnitude difference function, the average square difference function, the cross-correlation function and methods based on a combination of the above mentioned functions were applied.

13

Badania symulacyjne metod estymacji czasu opóźnienia sygnałów losowych wykorzystujących transformatę Hilberta

Hanus R., Zych M., Petryka L.

Przegląd Elektrotechniczny

|

2015

|

R. 91, nr 8

15--18

PL

W artykule przedstawiono wyniki badań czterech korelacyjnych metod estymacji czasu opóźnienia, w których zastosowano transformatę Hilberta. W symulacjach wykorzystano wybrane modele wzajemnie opóźnionych sygnałów stochastycznych. Uzyskane wyniki porównano z wynikami otrzymanymi dla klasycznej korelacji wzajemnej.

EN

The article presents the research results of the four correlation time delay estimation methods, in which the Hilbert Transform is applied. In the simulations selected models of mutually delayed stochastic signals were used. The obtained results were compared with the classical crosscorrelation procedure.

14

Niepewność standardowa oceny funkcji korelacji wzajemnej wyznaczanej metodą warunkowej wartości średniej modułu sygnału

Kowalczyk A., Szlachta A., Hanus R.

Przegląd Elektrotechniczny

|

2014

|

R. 90, nr 1

47--49

PL

W artykule przedstawiono zastosowanie warunkowej wartości średniej modułu sygnału do wyznaczania unormowanej funkcji korelacji wzajemnej Pxy (τ) skorelowanych sygnałów losowych o rozkładzie normalnym. Wykazano, że proponowana metoda charakteryzuje się mniejszą niepewnością standardową niż metoda bezpośrednia w zakresie 0,502≤ Pxy (τ)≤1. Podano przykład zastosowania omawianej metody do estymacji opóźnienia transportowego.

EN

The paper presents the use of the conditional expected value of the signal’s absolute value to determine the normalized cross-correlation Pxy (τ). It was shown that proposed method has a smaller standard uncertainty than the direct method in the range 0,502≤ Pxy (τ)≤1.

15

Badania symulacyjne wybranych statystycznych metod estymacji czasu opóźnienia sygnałów losowych

Hanus R.

Przegląd Elektrotechniczny

|

2014

|

R. 90, nr 12

52--55

PL

W artykule omówiono zastosowanie w pomiarach opóźnień czasowych sygnałów losowych następujących metod różnicowych: średniego modułu różnicy amplitud, średniego kwadratu różnicy amplitud oraz metod złożonych, będących połączeniem ww. metod różnicowych i funkcji korelacji wzajemnej. Dla przyjętych modeli sygnałów przeprowadzono badania symulacyjne i porównano niepewności standardowe estymacji czasu opóźnienia.

EN

This paper presents the use for time delay measurement of random signals such differential methods as the average magnitude difference function, the average square difference function and methods based on a combination of the above mentioned functions and cross-correlation. For the chosen model of signals the simulation was conducted and uncertainties of time delay estimation by use described methods were determined.

16

Practical application of cross correlation technique to measure jitter of master-oscillator-power-amplifier laser system

Młyńczak J., Sawicz-Kryniger K., Fry A. R., Glownia J. M., Leemans S.

Opto-Electronics Review

|

2014

|

Vol. 22, No. 4

218-223

EN

The Linac coherent light source (LCLS) at the SLAC National Accelerator Laboratory (SLAC) is the world’s first hard X-ray free electron laser (XFEL) and is capable of producing high-energy, femtosecond duration X-ray pulses. A common technique to study fast timescale physical phenomena, various “pump/probe” techniques are used. In these techniques there are two lasers, one optical and one X-ray, that work as a pump and as a probe to study dynamic processes in atoms and molecules. In order to resolve phenomena that occur on femtosecond timescales, it is imperative to have very precise timing between the optical lasers and X-rays (on the order of ~20 fs or better). The lasers are synchronized to the same RF source that drives the accelerator and produces the X-ray laser. However, elements in the lasers cause some drift and time jitter, thereby de-synchronizing the system. This paper considers cross-correlation technique as a way to quantify the drift and jitter caused by the regenerative amplifier of the ultrafast optical laser.

17

Cross-correlation-based method vs. classical FFT for spectral analysis of impulse response

Kotowski A.

Acta Mechanica et Automatica

|

2014

|

Vol. 8, no. 4

219--222

EN

The paper presents comparison of results of impulse response spectral analysis that has been obtained using a method based on cross-correlation with results obtained using classical FFT. The presented non-Fourier method is achieved by correlating the analyzed signal and reference single-harmonic signals and using Hilbert transform to obtain an envelope of cross-correlation. The envelope of cross correlation makes it possible to calculate appropriate indicator and make its plot in frequency domain as a spectrum. The spectrum obtained this way has its advantage over the FFT that the spectral resolution does not depend on duration of signal. At the same time, the spectral resolution can be much greater than spectral resolution resultant from FFT. Obtained results show that presented non-Fourier method gives frequency readout more accurate in comparison to FFT when the impulse response is a short-time signal e.g. few dozen of miliseconds lasting.

18

On reproducibility of relative locations of recurrent earthquakes recovered from similarity of their waveforms at a single station

Gnyp A.

Acta Geophysica

|

2014

|

Vol. 62, no. 6

1246--1261

EN

Relative locations of recurrent earthquakes can be recovered from values of cross-correlation coefficients between their waveforms at a single station, provided that an idea of Menke (1999) that the values depend inversely exponentially from separation between the sources is true. An algorithm developed in Gnyp (2013) based on this idea was applied here for recovering relative locations of the two groups of the 2005-2006 recurrent earthquakes in Mukacheve, Ukraine, from the sets of crosscorrelation coefficients between their records at the four local network stations to find out whether the locations were in principle reproducible independently at each of the stations, at epicentral distances from about 6 to 64 km. The resulting sets of locations occurred in good agreement with each other, which may be considered as an experimental evidence for validity of the Menke’s dependence over the corresponding range of distances. The reproducibility of relative locations has been analyzed in terms of existence and uniqueness of the inverse problem’s solution, and in connection with data completeness and the influence of noise on it.

19

Korelacyjne metody estymacji czasu opóźnienia sygnałów

Czopik G., Kraszewski T.

Elektronika : konstrukcje, technologie, zastosowania

|

2013

|

Vol. 54, nr 1

85-89

PL

Zagadnienie estymacji czasu opóźnienia sygnałów odgrywa ważną rolę w przetwarzaniu danych z wielu sensorów. Wartość opóźnienia pomiędzy sygnałami, zniekształcanymi przez szumy oraz zakłócenia, odebranymi przez odseparowane od siebie stacjonarne lub mobilne sensory, jest bardzo użytecznym parametrem dla aplikacji, które wykorzystywane są w wielu dziedzinach: przetwarzaniu sygnałów radarowych, rozpoznaniu sygnałowym, analizie mowy i lokalizacji jej źródła, geofizyce, inżynierii biomedycznej i wielu innych. Występuje wiele algorytmów estymacji czasu opóźnienia, a metoda korelacji wzajemnej jest jednym z podstawowych rozwiązań tego problemu. Wiele innych bardziej rozbudowanych metod bazuje na tym algorytmie. Wykorzystuje ona korelację sygnałów z odseparowanych sensorów i rozpatruje argument czasu odpowiadający maksymalnej wartości funkcji na wyjściu (pikowi). Jest to estymowany czas opóźnienia. W celu poprawy detekcji piku, po przeprowadzeniu operacji matematycznych korelacji wzajemnej, sugerowane jest wykorzystanie różnorodnych funkcji skalujących (ważących). Takie techniki, nazywane dla odróżnienia uogólnioną korelacją wzajemną, są popularnymi rozwiązaniami dla estymacji opóźnień czasowych z powodu ich dokładności, jak również umiarkowanej złożoności obliczeniowej. Metody te mają również pewne wady, dostarczają niejednoznacznych rezultatów dla szumów, zniekształceń skorelowanych z pożądanymi sygnałami. W artykule przybliżone zostaną korelacyjne metody estymacji czasu opóźnienia sygnałów oraz zaprezentowane wstępne wyniki ich badań symulacyjnych porównane pod względem dokładności estymacji parametru czasowego oraz szybkości działania w różnych warunkach pomiarowych.

EN

The problem of estimating the time delay (TDE) between signals received at two spatially separated sensors in the presence of jamming or noise is considered for a variety of applications, such as in radar signals processing, speech analysis and localization, geophysics, biomedical engineering and many others.There are a lot of algorithms to estimate the time delay. The basic cross - correlation (BCC) method is one of the essential solution of the time delay estimation problem. Many other time delay estimation developed methods based on this algorithm. This technique makes use of signals correlation and considers the time argument that corresponds to the maximum peak in the output as the estimated time delay. To improve the peak detection is suggested to use the various weighting functions after the cross - correlation. This technique is called generalized cross - correlation (GCC). The GCC method is the most popular technique for TDE due to their accuracy and moderate computational complexity. On the other hand they yield ambiguous results when the noises at the two sensors are correlated with the desired signals. In this article we described the cross correlation methods of time delay estimation and we presented the preliminary results of simulation research. Their effects are compared in respect of time parameter estimation accuracy and computation complexity in the different measurement conditions.

20

Recovering relative locations of the 2005-2006 Mukacheve earthquakes from similarity of their waveforms at a single station

Gnyp A.

Acta Geophysica

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2013

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Vol. 61, no. 5

1074--1087

EN

An algorithm was designed for inverting the set of cross-correlation coefficients between the records of recurrent earthquakes by a single station for their relative locations based on an assumption of Menke (1999) that the cross-correlation is only a function of separation between the sources and decays exponentially with it. Tested on synthetic data sets, the algorithm easily recovered the true relative locations, the initial ones seeded randomly. Inversion of the cross-correlation coefficients between the records of the two groups of the Mukacheve 2005–2006 recurrent earthquakes by the station Mukacheve steadily produced an almost flat shape of hypocenter cloud for each of the groups, final relative locations of hypocenters being almost the same for different initial seedlings. The combined set of cross-correlation coefficients for both groups was also inverted, and the shape of the combined hypocenter cloud was almost flat again. These results compare well with ones obtained earlier (Gnyp 2010) by relocating the Mukacheve earthquakes with the use of differential arrivals and source specific station terms.