- Email: [email protected]
Obtaining “images” from iron objects using a 3-axis fluxgate magnetometer
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109 www.elsevier.com/locate/nima
Obtaining ‘‘images’’ from iron objects using a 3-axis fluxgate magnetometer Jose´ Chiloa, Abbas Jaborb, Ludwik Lizskac, A˚ge J. Eided, Thomas Lindbladb, a
University of Ga¨vle, S-80176 Ga¨vle, Sweden Royal Institute of Technology, Department of Physics, S-106 91 Stockholm, Sweden c Swedish Institute of Space Physics in Umea˚, Sweden d Ostfold University College, N-1757 Halden, Norway
b
Available online 29 June 2007
Abstract Magnetic objects can cause local variations in the Earth’s magnetic field that can be measured with a magnetometer. Here we used triaxial magnetometer measurements and an analysis method employing wavelet techniques to determine the ‘‘signature’’ or ‘‘fingerprint’’ of different iron objects. Clear distinctions among the iron samples were observed. The time-dependent changes in the frequency powers were extracted by use of the Morlet wavelet corresponding to frequency bands from 0.1 to 100 Hz. r 2007 Elsevier B.V. All rights reserved. Keywords: Magnetometer; Feature extraction; Wavelets; Fingerprints
1. Introduction This paper describes possible ways to extract and enhance features in magnetometer signals to obtain a signature or fingerprint of different shaped iron objects. A miniature tri-axial magnetometer and wavelet analysis methods are used. Although small magnetometers are used in a variety of applications (e.g. process control, security systems, compassing, traffic and vehicle detection, etc. [1–2]), very little is done in the field with regard to searching for and identifying specific objects. Magnetometers have been used to detect archeological sites, shipwrecks and other buried or submerged objects [3], but they rarely involve the automatic feature extraction and ‘‘fingerprint’’ identification capability that we aim for in the present paper. We would like to develop a small and easy to use integrated sensor system from which we can obtain fingerprints from the inherent signal features characteristic for particular iron objects. An example of an application for such a system would be to use a small vehicle (e.g. a small UAV) to search for metallic objects of different shapes. Corresponding author. Tel.: +46 8 16 11 09; fax: +46 8 15 86 74.
E-mail address: [email protected] (T. Lindblad). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.06.070
In this study, the continuous wavelet transform is used as a pre-processor and feature extractor. The wavelet transform has become a powerful tool for frequency analysis, especially for non-stationary time series as in this case. The continuous wavelet transform of a function y(t) is defined as (here * denotes complex conjugation) [4]: wða; bÞ ¼ a1=2
Z
1
yðtÞg ððt bÞ=aÞ dt
(1)
1
where variable a is the scale dilation parameter and b the translation parameter. Both parameters are dimensionless. The real- or complex-valued function g(t) is called a mother (or analyzing) wavelet. Here a particular wavelet transform, the Morlet wavelet, is used. This wavelet gives the smallest time-bandwidth product. The results from the continuous wavelet transform are used to compute the ampligram. The ampligram is a technique, which may be used to separate independent components of the signal, assuming that the different components are characterized by different spectral densities. The experience from studies of oscillations in complex mechanical systems indicates that a given oscillation mode usually occurs with a certain amplitude/spectral density. The amplitude ratios between
ARTICLE IN PRESS 1106
J. Chilo et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109
possible modes are usually constant in such a system. This was one of the reasons for creating this filtering technique.
2. Experimental setup and results 2.1. Measurement practice In this study we use a miniature 3-axis fluxgate magnetometer (model 533, manufacturer Applied Physics System [5]). The magnetometer is packaged in a cylindrical fiberglass package of dimensions 0.72500 dia 1.500 long. The 3-axis fluxgate magnetometer provides three analog output voltages proportional to the magnetic field in three orthogonal directions. Full scale output is 74.0 V; this voltage represents a magnetic field of 71.00 G (0.1 mT). The system noise level is 3 106G RMS/Hz1/2 (0.3 nT RMS/Hz1/2).
A typical fluxgate sensor consists of a core of magnetic material surrounded by two coils of wire, Fig. 1A, [1]. A current is sent through the primary wire, which both induces a voltage in the secondary wire and magnetizes the core material. The primary winding employs an alternating current to drive the core cyclically into magnetic saturation. An electromotive force will be developed in the secondary winding, the strength of which is a function of the level of the magnetic field parallel to this winding. Thus, the voltage inside the secondary loop is an AC voltage and is due to the current through the primary winding, which is magnetizing the magnetic core and the external magnetic field along its axis. The level of an ambient magnetic field is sensed by the fluxgate element along the axis of its secondary winding. A magnetic field along the secondary coil axis will cause an electromotive force to develop with amplitude directly proportional to the magnitude of the field, while the second harmonic
Fig. 1. (A) Internal workings of a fluxgate magnetic sensor and (B) the magnetometer experiment.
Fig. 2. (A) Iron samples and (B) the three signals from the magnetometer showing five events: wagon only (0–20 s), sample A (20–40 s), sample B (40–60 s), sample C (60–80 s), sample D (80–100 s). The top figure is for the y-axis, the middle the x-axis and the bottom the z-axis.
ARTICLE IN PRESS J. Chilo et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109
output of the sensor will be practically zero when there is no ambient field. Thus, the fluxgate magnetometer is capable of measuring the strength of any component of the Earth’s magnetic field by simply reorienting the instrument so that the cores are parallel to the desired component. Fluxgate magnetometers are suitable for measurements from zero up to 2 mT (20 G) and can have a resolution of better than 1 nT (10 mG) with a noise of a few pT. These are relatively simple instruments to construct, hence they are relatively inexpensive. Fig. 1B displays how the magnetometer experiment was implemented. A battery powered motor and a non-metallic wagon were used to move the iron samples in the magnetometer surroundings in order to distort the magnetic field. For the determination of magnetic properties, we prepared four iron samples (edge 2.5 cm, thickness 1.0–1.5 cm) as shown in Fig. 2A. The iron samples have
1107
four different shapes, labeled here A, B, C, and D. The experiment was performed in normal office surroundings, where the background variation of magnetic flux density is usually lower than 5nT during one measurement, which takes less than 2 min [6]. The noise level (0.3 nT RMS/Hz1/2) of our fluxgate magnetometer is clearly lower than the background variation. Magnetometer data taken during 120 s (five turns) are presented in Fig. 2B. During the measuring procedure a sample is placed on the wagon at every turn. The data from z-axis show clearly the presence of the samples. These data are used in the analysis described below. 2.2. Wavelet transform methods The signals from the magnetometer are processed using various methods developed over the years by the Swedish Space Institute (IRF) at Umea˚ [4,7,8]. These methods
Fig. 3. The original time series and the reconstructed time series from ampligram of the four different shaped iron samples (A). The scalogram (B), the ampligram (C) and the time-scale spectrum (D). A scalogram displays the wavelet coefficient magnitude as a function of the time scale (inverted frequency) and of the elapsed time. It may be seen in (B) the structures of the scalograms for samples.
ARTICLE IN PRESS 1108
J. Chilo et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109
involve the Morlet wavelet transform, the ampligram and the time-scale spectrum. The ampligram may be considered as analogous to signal decomposition into Fourier components. Different components correspond to different wavelet coefficient magnitudes and thus provide information similar to spectral densities. To obtain non-linear filtering, a wavelet frequency spectrum of the time series is calculated. A kind of band-pass filtering of wavelet coefficient magnitudes is performed, resulting in inverse wavelet transforms to get new time-signals. Each new time-signal is what the signal would look like if only a narrow range of wavelet coefficient amplitude would be present in the time series. With new time-signals as rows, a matrix Z is constructed. This matrix Z is the ampligram of the original time series. The summation along columns of the matrix Z should result in the original time series if there was no energy leakage from the filter band. Fig. 3 shows the original time series and the reconstructed time series from ampligram of the four iron samples shown in position (a) in each set of four diagrams. It may be seen that the differences between the observed and reconstructed data are of the order of a
few percent, which means that energy leakage from outside the pass-band is not very important. We observe that the amplitude in the reconstructed signals is relative (no offset left). The ampligram is a useful method of presentation of the physical properties of the time series. The ampligram demonstrates the amplitude and phase of components of the signals corresponding to different spectral densities. The ampligram of the A sample in Fig. 3 with lowest coefficient magnitudes (0–30%) is burst-like and random. A regular structure seems to be dominant at about 2 s in the ampligram. In addition to the ampligram, a time-scale spectrum is defined using a forward wavelet transform of each row in the ampligram. The time-scale spectrum of the ampligram tells us more than the original wavelet spectrum does. The time-scale spectrum reveals individual signal components and indicates the statistical properties of each component: deterministic or stochastic. The time-scale spectrum is calculated as follows. Each row of the ampligram matrix, Z, is wavelet transformed, resulting in M matrices. We then time-average these
Fig. 4. The wavelet power spectrum of the iron samples (A–D).
ARTICLE IN PRESS J. Chilo et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109
matrices (average along rows) leading to M arrays. With new arrays as rows, a matrix Y is constructed. This matrix Y is the time-scale spectrum. The time-scale spectrum will generate a 3D graph showing the time scale of the signal on the x-axis, the wavelet coefficient magnitude of the original signal, in percent of its max value, on the y-axis and the wavelet coefficient magnitude of the decomposed component as the color scale. The interesting property of this graph is that deterministic or semi-periodic structures in the data are mapped on the graph as vertically elongate features, while purely stochastic structures are mapped as horizontally elongated features. We can see in Fig. 3 the structures of the time-scale spectrum for the four iron samples at position (d) in the sets of four diagrams. 2.3. Wavelet power (frequency range) A power spectrum can be calculated from the result of a wavelet transform. The power analysis computes the power of the wavelet transform spectrum across time for a specified frequency band by integrating the interpolated wavelet spectrum surface [9,10]. The Morlet wavelet is used for this spectral analysis. The wavelet spectrum frequency range is a specialized wavelet procedure that combines the wavelet transform and this power analysis into a single step, see Fig. 4. We can see in Figs. 4 that the curves of the wavelet power spectrum frequency range are more regular for the A and C iron samples. The B and D iron samples have a more complicate shape. The integration is carried out in time steps that span the full time range of the data. The powers will each reflect a time increment dt ¼ (time range)/(time steps). In this study the spectrum is plotted using the power format: Time-Integral Squared Amplitude power, 2*dx*(Re2+Im2), where Re is the real component of the wavelet transform at a given time and frequency, Im is the imaginary component and dx is the sampling interval. We should note that the power curve represents snapshots in time of the power in the signal between the frequencies specified. It is not a cumulative curve. The peaks in the power curve are identified by a local maxima
1109
detection algorithm. The frequencies use a logarithmic spacing. This is useful when most of a signal’s energy is at lower frequencies. 3. Summary In this study, distinguishing features of iron samples of four different shapes were determined using wavelet methods. Systematic differences were observed between the magnetic properties of the four shaped iron samples. The time-dependent changes in the frequency powers were extracted by the use of the Morlet wavelet corresponding to frequency bands from 0.1 to 100 Hz. The results show reduced power spectrum in the B and D iron samples, compared with A and C iron samples. Acknowledgment The authors would like to thank Dr. Clark S. Lindsey for valuable comments and for reading the manuscript. References [1] C. Bredeson, M. Connors, Enhancing the study of the aurora using low-cost magnetometer, Can. Undergraduate Physi. J. 2 (2) (2004). [2] mPhase, /http://www.mphasetech.comS. [3] A. Clark, Seeing Beneath the Soil: Prospecting Methods in archaeology, revised Ed., BT Batsford Ltd., London, 1996, ISBN 0415214408. [4] L. Liszka, Decomposition of infrasonic signals using a wavelet transform, J. Low Freq. Sound Vib. 18 (2) (1999). [5] Applied Physics Systems, /http://www.appliedphysics.com/S. [6] L. Eskola, R. Puranen, H. Soininen, Measurement of magnetic properties of steel sheets, Geophys. Prospect. 47 (1999) 593–602. [7] L. Liszka, Cognitive Information Processing in Space Physics and Astrophysics, Pachart Publishing House, Tucson, AZ, USA, 2003, ISBN 0-88126-090-8. [8] J. Chilo, A. Jabor, L. Liszka, Th. Lindblad, Filtering and Extracting Features from Infrasound Data, in: IEEE-NPSS Real Time Conference, June 4–10, 2005, pp. 451–455. [9] I. Kaplan, Wavelets and signal processing, 2003, /http://www. bearcave.com/misl/misl_tech/wavelets/index.htmlS. [10] Cranes software /http://www.systat.com/products/AutoSignal/help/ ?sec-=1097aS.
Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109 www.elsevier.com/locate/nima
Obtaining ‘‘images’’ from iron objects using a 3-axis fluxgate magnetometer Jose´ Chiloa, Abbas Jaborb, Ludwik Lizskac, A˚ge J. Eided, Thomas Lindbladb, a
University of Ga¨vle, S-80176 Ga¨vle, Sweden Royal Institute of Technology, Department of Physics, S-106 91 Stockholm, Sweden c Swedish Institute of Space Physics in Umea˚, Sweden d Ostfold University College, N-1757 Halden, Norway
b
Available online 29 June 2007
Abstract Magnetic objects can cause local variations in the Earth’s magnetic field that can be measured with a magnetometer. Here we used triaxial magnetometer measurements and an analysis method employing wavelet techniques to determine the ‘‘signature’’ or ‘‘fingerprint’’ of different iron objects. Clear distinctions among the iron samples were observed. The time-dependent changes in the frequency powers were extracted by use of the Morlet wavelet corresponding to frequency bands from 0.1 to 100 Hz. r 2007 Elsevier B.V. All rights reserved. Keywords: Magnetometer; Feature extraction; Wavelets; Fingerprints
1. Introduction This paper describes possible ways to extract and enhance features in magnetometer signals to obtain a signature or fingerprint of different shaped iron objects. A miniature tri-axial magnetometer and wavelet analysis methods are used. Although small magnetometers are used in a variety of applications (e.g. process control, security systems, compassing, traffic and vehicle detection, etc. [1–2]), very little is done in the field with regard to searching for and identifying specific objects. Magnetometers have been used to detect archeological sites, shipwrecks and other buried or submerged objects [3], but they rarely involve the automatic feature extraction and ‘‘fingerprint’’ identification capability that we aim for in the present paper. We would like to develop a small and easy to use integrated sensor system from which we can obtain fingerprints from the inherent signal features characteristic for particular iron objects. An example of an application for such a system would be to use a small vehicle (e.g. a small UAV) to search for metallic objects of different shapes. Corresponding author. Tel.: +46 8 16 11 09; fax: +46 8 15 86 74.
E-mail address: [email protected] (T. Lindblad). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.06.070
In this study, the continuous wavelet transform is used as a pre-processor and feature extractor. The wavelet transform has become a powerful tool for frequency analysis, especially for non-stationary time series as in this case. The continuous wavelet transform of a function y(t) is defined as (here * denotes complex conjugation) [4]: wða; bÞ ¼ a1=2
Z
1
yðtÞg ððt bÞ=aÞ dt
(1)
1
where variable a is the scale dilation parameter and b the translation parameter. Both parameters are dimensionless. The real- or complex-valued function g(t) is called a mother (or analyzing) wavelet. Here a particular wavelet transform, the Morlet wavelet, is used. This wavelet gives the smallest time-bandwidth product. The results from the continuous wavelet transform are used to compute the ampligram. The ampligram is a technique, which may be used to separate independent components of the signal, assuming that the different components are characterized by different spectral densities. The experience from studies of oscillations in complex mechanical systems indicates that a given oscillation mode usually occurs with a certain amplitude/spectral density. The amplitude ratios between
ARTICLE IN PRESS 1106
J. Chilo et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109
possible modes are usually constant in such a system. This was one of the reasons for creating this filtering technique.
2. Experimental setup and results 2.1. Measurement practice In this study we use a miniature 3-axis fluxgate magnetometer (model 533, manufacturer Applied Physics System [5]). The magnetometer is packaged in a cylindrical fiberglass package of dimensions 0.72500 dia 1.500 long. The 3-axis fluxgate magnetometer provides three analog output voltages proportional to the magnetic field in three orthogonal directions. Full scale output is 74.0 V; this voltage represents a magnetic field of 71.00 G (0.1 mT). The system noise level is 3 106G RMS/Hz1/2 (0.3 nT RMS/Hz1/2).
A typical fluxgate sensor consists of a core of magnetic material surrounded by two coils of wire, Fig. 1A, [1]. A current is sent through the primary wire, which both induces a voltage in the secondary wire and magnetizes the core material. The primary winding employs an alternating current to drive the core cyclically into magnetic saturation. An electromotive force will be developed in the secondary winding, the strength of which is a function of the level of the magnetic field parallel to this winding. Thus, the voltage inside the secondary loop is an AC voltage and is due to the current through the primary winding, which is magnetizing the magnetic core and the external magnetic field along its axis. The level of an ambient magnetic field is sensed by the fluxgate element along the axis of its secondary winding. A magnetic field along the secondary coil axis will cause an electromotive force to develop with amplitude directly proportional to the magnitude of the field, while the second harmonic
Fig. 1. (A) Internal workings of a fluxgate magnetic sensor and (B) the magnetometer experiment.
Fig. 2. (A) Iron samples and (B) the three signals from the magnetometer showing five events: wagon only (0–20 s), sample A (20–40 s), sample B (40–60 s), sample C (60–80 s), sample D (80–100 s). The top figure is for the y-axis, the middle the x-axis and the bottom the z-axis.
ARTICLE IN PRESS J. Chilo et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109
output of the sensor will be practically zero when there is no ambient field. Thus, the fluxgate magnetometer is capable of measuring the strength of any component of the Earth’s magnetic field by simply reorienting the instrument so that the cores are parallel to the desired component. Fluxgate magnetometers are suitable for measurements from zero up to 2 mT (20 G) and can have a resolution of better than 1 nT (10 mG) with a noise of a few pT. These are relatively simple instruments to construct, hence they are relatively inexpensive. Fig. 1B displays how the magnetometer experiment was implemented. A battery powered motor and a non-metallic wagon were used to move the iron samples in the magnetometer surroundings in order to distort the magnetic field. For the determination of magnetic properties, we prepared four iron samples (edge 2.5 cm, thickness 1.0–1.5 cm) as shown in Fig. 2A. The iron samples have
1107
four different shapes, labeled here A, B, C, and D. The experiment was performed in normal office surroundings, where the background variation of magnetic flux density is usually lower than 5nT during one measurement, which takes less than 2 min [6]. The noise level (0.3 nT RMS/Hz1/2) of our fluxgate magnetometer is clearly lower than the background variation. Magnetometer data taken during 120 s (five turns) are presented in Fig. 2B. During the measuring procedure a sample is placed on the wagon at every turn. The data from z-axis show clearly the presence of the samples. These data are used in the analysis described below. 2.2. Wavelet transform methods The signals from the magnetometer are processed using various methods developed over the years by the Swedish Space Institute (IRF) at Umea˚ [4,7,8]. These methods
Fig. 3. The original time series and the reconstructed time series from ampligram of the four different shaped iron samples (A). The scalogram (B), the ampligram (C) and the time-scale spectrum (D). A scalogram displays the wavelet coefficient magnitude as a function of the time scale (inverted frequency) and of the elapsed time. It may be seen in (B) the structures of the scalograms for samples.
ARTICLE IN PRESS 1108
J. Chilo et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109
involve the Morlet wavelet transform, the ampligram and the time-scale spectrum. The ampligram may be considered as analogous to signal decomposition into Fourier components. Different components correspond to different wavelet coefficient magnitudes and thus provide information similar to spectral densities. To obtain non-linear filtering, a wavelet frequency spectrum of the time series is calculated. A kind of band-pass filtering of wavelet coefficient magnitudes is performed, resulting in inverse wavelet transforms to get new time-signals. Each new time-signal is what the signal would look like if only a narrow range of wavelet coefficient amplitude would be present in the time series. With new time-signals as rows, a matrix Z is constructed. This matrix Z is the ampligram of the original time series. The summation along columns of the matrix Z should result in the original time series if there was no energy leakage from the filter band. Fig. 3 shows the original time series and the reconstructed time series from ampligram of the four iron samples shown in position (a) in each set of four diagrams. It may be seen that the differences between the observed and reconstructed data are of the order of a
few percent, which means that energy leakage from outside the pass-band is not very important. We observe that the amplitude in the reconstructed signals is relative (no offset left). The ampligram is a useful method of presentation of the physical properties of the time series. The ampligram demonstrates the amplitude and phase of components of the signals corresponding to different spectral densities. The ampligram of the A sample in Fig. 3 with lowest coefficient magnitudes (0–30%) is burst-like and random. A regular structure seems to be dominant at about 2 s in the ampligram. In addition to the ampligram, a time-scale spectrum is defined using a forward wavelet transform of each row in the ampligram. The time-scale spectrum of the ampligram tells us more than the original wavelet spectrum does. The time-scale spectrum reveals individual signal components and indicates the statistical properties of each component: deterministic or stochastic. The time-scale spectrum is calculated as follows. Each row of the ampligram matrix, Z, is wavelet transformed, resulting in M matrices. We then time-average these
Fig. 4. The wavelet power spectrum of the iron samples (A–D).
ARTICLE IN PRESS J. Chilo et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1105–1109
matrices (average along rows) leading to M arrays. With new arrays as rows, a matrix Y is constructed. This matrix Y is the time-scale spectrum. The time-scale spectrum will generate a 3D graph showing the time scale of the signal on the x-axis, the wavelet coefficient magnitude of the original signal, in percent of its max value, on the y-axis and the wavelet coefficient magnitude of the decomposed component as the color scale. The interesting property of this graph is that deterministic or semi-periodic structures in the data are mapped on the graph as vertically elongate features, while purely stochastic structures are mapped as horizontally elongated features. We can see in Fig. 3 the structures of the time-scale spectrum for the four iron samples at position (d) in the sets of four diagrams. 2.3. Wavelet power (frequency range) A power spectrum can be calculated from the result of a wavelet transform. The power analysis computes the power of the wavelet transform spectrum across time for a specified frequency band by integrating the interpolated wavelet spectrum surface [9,10]. The Morlet wavelet is used for this spectral analysis. The wavelet spectrum frequency range is a specialized wavelet procedure that combines the wavelet transform and this power analysis into a single step, see Fig. 4. We can see in Figs. 4 that the curves of the wavelet power spectrum frequency range are more regular for the A and C iron samples. The B and D iron samples have a more complicate shape. The integration is carried out in time steps that span the full time range of the data. The powers will each reflect a time increment dt ¼ (time range)/(time steps). In this study the spectrum is plotted using the power format: Time-Integral Squared Amplitude power, 2*dx*(Re2+Im2), where Re is the real component of the wavelet transform at a given time and frequency, Im is the imaginary component and dx is the sampling interval. We should note that the power curve represents snapshots in time of the power in the signal between the frequencies specified. It is not a cumulative curve. The peaks in the power curve are identified by a local maxima
1109
detection algorithm. The frequencies use a logarithmic spacing. This is useful when most of a signal’s energy is at lower frequencies. 3. Summary In this study, distinguishing features of iron samples of four different shapes were determined using wavelet methods. Systematic differences were observed between the magnetic properties of the four shaped iron samples. The time-dependent changes in the frequency powers were extracted by the use of the Morlet wavelet corresponding to frequency bands from 0.1 to 100 Hz. The results show reduced power spectrum in the B and D iron samples, compared with A and C iron samples. Acknowledgment The authors would like to thank Dr. Clark S. Lindsey for valuable comments and for reading the manuscript. References [1] C. Bredeson, M. Connors, Enhancing the study of the aurora using low-cost magnetometer, Can. Undergraduate Physi. J. 2 (2) (2004). [2] mPhase, /http://www.mphasetech.comS. [3] A. Clark, Seeing Beneath the Soil: Prospecting Methods in archaeology, revised Ed., BT Batsford Ltd., London, 1996, ISBN 0415214408. [4] L. Liszka, Decomposition of infrasonic signals using a wavelet transform, J. Low Freq. Sound Vib. 18 (2) (1999). [5] Applied Physics Systems, /http://www.appliedphysics.com/S. [6] L. Eskola, R. Puranen, H. Soininen, Measurement of magnetic properties of steel sheets, Geophys. Prospect. 47 (1999) 593–602. [7] L. Liszka, Cognitive Information Processing in Space Physics and Astrophysics, Pachart Publishing House, Tucson, AZ, USA, 2003, ISBN 0-88126-090-8. [8] J. Chilo, A. Jabor, L. Liszka, Th. Lindblad, Filtering and Extracting Features from Infrasound Data, in: IEEE-NPSS Real Time Conference, June 4–10, 2005, pp. 451–455. [9] I. Kaplan, Wavelets and signal processing, 2003, /http://www. bearcave.com/misl/misl_tech/wavelets/index.htmlS. [10] Cranes software /http://www.systat.com/products/AutoSignal/help/ ?sec-=1097aS.