On application of the Fourier Transform Band Pass Filtering technique

• Autorzy: Popiński W.

Identyfikatory

DOI

10.2478/v10018-009-0026-3

• Języki publikacji: EN

Abstrakty

EN

In this work theoretical aspects of the Fourier Transform Band Pass Filter (FTBPF) technique are investigated which show that such a procedure is applicable to extraction of irregular monochromatic oscillations with time-varying amplitudes from the analyzed signal data. Considerations concerning the boundary effects occurring in numerical implementation of the FTBPF are included which indicate that the filter transfer function smoothness influences boundary effects magnitude. The possibility of using the studied filtration technique for recognition of elliptical oscillation polarization is envisaged and an estimate of oscillation polarization classification error is derived.

Słowa kluczowe

EN

Transform Band Pass Filter; transmittance function; irregular oscillation; boundary effects; oscillation polarization

• Wydawca: Centrum Badań Kosmicznych PAN ; De Gruyter
• Czasopismo: Artificial Satellites : Journal of Planetary Geodesy
• Rocznik: 2009
• Tom: Vol. 44, No. 4
• Strony: 149--160
• Opis fizyczny: Bibliogr. 44 poz., wykr.

Twórcy

autor

Popiński W.

• Space Research Centre PAS

Bibliografia

• Blackledge J.M. (2003) Digital Signal Processing, Horwood Publishing, Chichester, West Sussex, England.
• Bremaud P. (2002) Mathematical Principles of Signal Processing: Fourier and Wavelet Analysis, Springer Verlag Inc., New York.
• Brillinger D.R. (1975) Time Series - Data Analysis and Theory, Holt, Rinehart and Winston Inc., New York.
• Devroye L., Györfi L., Lugosi G. (1996) A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New York.
• Dong D., Zheng D. (1985) The End Effects of Vondrak Filter, Annals of Shanghai Observatory - Academia Sinica, Vol. 7, 13-25.
• Evans J.C. (1985) Selection of a Numerical Filtering Method: Convolution or Transform Windowing, Journal of Geophysical Research, Vol. 90, No. C3, 4991-4994.
• Fabert O. (2004) Effiziente Wavelet Filterung mit hoher Zeit-Frequenz-Auflösung, Veröffentlichungen der Deutschen Geodätischen Kommission, Reihe A - Theoretische Geodäsie, Heft 119, Verlag der Bayerischen Akademie der Wissenschaften, München.
• Fabert O., Schmidt M. (2003) Wavelet Filtering with High Time-Frequency Resolution and Effective Numerical Implementation Applied on Polar Motion, Artificial Satellites – Journal of Planetary Geodesy, Vol. 38, No. 1, 3-13.
• Ferreira P.J.S.G., and Kempf A. (2006) Superoscillations: Faster Than the Nyquist Rate, IEEE Transactions on Signal Processing, Vol. 54, No. 10, 3732-3740.
• Forbes A.M.G. (1988) Fourier Transform Filtering: A Cautionary Note, Journal of Geophysical Research, Vol. 93, No. C6, 6958-6962.
• Gasquet C., Witomski P. (1999) Fourier Analysis and Applications - Filtering, Numerical Computation, Wavelets, Springer Verlag Inc., New York.
• Hasan T. (1983) Complex Demodulation: Some Theory and Applications, In Brillinger D.R. and Krishnaiah P.R. (Editors), Handbook of Statistics, Vol. 3 - Time Series in the Frequency Domain, Elsevier Science Publishers, Amsterdam, 125-156.
• Hoggar S.D. (2006) Mathematics of Digital Images - Creation, Compression, Restoration, Recognition, Cambridge University Press, Cambridge.
• Höpfner J. (1996) Seasonal Oscillation in Length-of-Day, Astronomische Nachrichten, Vol. 317, Nr. 4, 273-280.
• Jochmann H., Felsmann E. (2001) Evidence and Cause of Climate Cycles in Polar Motion, Journal of Geodesy, Vol. 74, No. 10, 711-719.
• Johnson N.L., Kotz S., Balakrishnan N. (1994) Continuous Univariate Distributions, Vol. 1, John Wiley & Sons Inc., New York.
• Kołaczek B. (1992) Variations of Short Periodical Oscillations of Polar Motion with Periods Ranging from 10-140 Days, Report No. 419, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, Ohio, USA.
• Kołaczek B. and Kosek W. (1993) Variations of 80-120 Days Oscillations of Polar Motion and Atmospheric Angular Momentum, Proceedings of the 7th International Symposium - Geodesy and Physics of the Earth, IAG Symposium No. 112, Potsdam, Germany, 5-10 October 1992, Edited by H. Montag and Ch. Reigber, Springer Verlag, 439-442.
• Koopmans L.H. (1974) Spectral Analysis of Time Series, Academic Press, New York.
• Kosek W. (1987) Computation of Short Periodical Variations of Pole Coordinates Using Maximum Entropy Spectral Analysis and an Ormsby Filter, Bulletin Géodésique, Vol. 61, No. 2, 109-124.
• Kosek W. (1995) Time Variable Band Pass Filter Spectra of Real and Complex-Valued Polar Motion Series, Artificial Satellites - Planetary Geodesy, Vol. 30, No. 1, 27-43.
• Kosek W. (2004) Possible Excitation of the Chandler Wobble by Variable Geophysical Annual Cycle, Artificial Satellites - Journal of Planetary Geodesy, Vol. 39, No. 2, 135-145.
• Kosek W., Kaczkowski J. (1994) Short Periodic Oscillations in x and y Pole Coordinates of the SLR and VLBI Techniques Detected After Filtering with the Kalman Filter, Proceedings of the 3rd Orlov Conference - Study of the Earth as Planet by Methods of Astronomy, Astrophysics and Geodesy, Odessa, 1992, Main Astronomical Observatory, Kiev, 288-297.
• Kosek W., Nastula J., Kołaczek B. (1995), Variability of Polar Motion Oscillations with Periods from 20 to 150 Days in 1979-1991, Bulletin Géodésique, Vol. 69, 308-319.
• Kosek W., Popiński W. (1999) Comparison of Spectro-Temporal Analysis Methods on Polar Motion and its Atmospheric Excitation, Artificial Satellites – Journal of Planetary Geodesy, Vol. 34, No. 2, 65-75.
• Liao D.C., Liao X.H. (2001) Comparison of Deformation at Ends of the Results Obtained by Some Commonly Used Filters, Annals of Shanghai Observatory - Academia Sinica, Vol. 22, 50-56.
• Nastula J., Korsun A., Kołaczek B., Kosek W., Hozakowski W. (1993) Variations of the Chandler and Annual Wobbles of Polar Motion in 1846-1988 and their Prediction, Manuscripta Geodaetica, Vol. 18, 131-135.
• Newland D.E. (1998) Time-Frequency and Time-Scale Signal Analysis by Harmonic Wavelets, In Procházka A., Uhliř J., Rayner P.J., Kingsbury N.G. (Editors), Signal Analysis and Prediction, Birkhäuser, Boston, 3-26.
• Pan Ch. (1998) Spectral Ringing Suppression and Optimal Windowing for Attenuation and Q Measurements, Geophysics, Vol. 63, No. 2, 632-636.
• Pan Ch. (2001) Gibbs Phenomenon Removal and Digital Filtering Directly through the Fast Fourier Transform, IEEE Transactions on Signal Processing, Vol. 49, No. 2, 444-448.
• Park J. (1992) Envelope Estimation for Quasi-Periodic Geophysical Signals in Noise: A Multi-taper Approach, In Walden A.T. and Guttorp P. (Editors), Statistics in the Environmental and Earth Sciences, London, 189-219.
• Popiński W. (1997) On Consistency of Discrete Fourier Analysis of Noisy Time Series, Artificial Satellites - Journal of Planetary Geodesy, Vol. 32, No. 3, 131-142.
• Popiński W. (2008) Insight into the Fourier Transform Band Pass Filtering Technique, Artificial Satellites - Journal of Planetary Geodesy, Vol. 43, No. 4, 129-141.
• Popiński W., Kosek W. (1995) The Fourier Transform Band Pass Filter and its Application for Polar Motion Analysis, Artificial Satellites - Planetary Geodesy, Vol. 30, No. 1, 9-25.
• Popiński W., Kosek W. (1999) Spectral Analysis of Sea Surface Topography Observed by TOPEX/POSEIDON Altimetry Using Two-Dimensional Fourier Transform, Report Nr 40 - Space Research Centre PAS, Warsaw 1999.
• Popiński W., Kosek W. (2000) Comparison of Various Spectro-Temporal Coherence Functions between Polar Motion and Atmospheric Excitation Functions, Artificial Satellites - Journal of Planetary Geodesy, Vol. 35, No. 4, 191-207.
• Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T. (1992) Numerical Recipes - The Art of Scientific Computing, Cambridge University Press, Cambridge.
• Schmitz-Hübsch H. and Schuh H (1999) Seasonal and Short-Period Fluctuations of Earth Rotation Investigated by Wavelet Analysis, In F. Krumm and V.S. Schwarze (eds), Quo vadis Geodesia…?, Technical Report Nr. 1999.6-1, Department of Geodesy and Geoinformatics, Universität Stuttgart, 421-431.
• Speed T.P. (1985) Some Practical and Statistical Aspects of Filtering and Spectrum Estimation, In Price J. F. (Editor), Fourier Techniques and Applications, Plenum Press, New York, 101-118.
• Torrence Ch. and Compo G.P. (1998) A Practical Guide to Wavelet Analysis, Bulletin of the American Meteorological Society, Vol. 79, No. 1, 61-78.
• Zheng D.W., Dong D.N. (1986) Realization of Narrow Band Filtering of the Polar Motion Data with Multi-Stage Filter, Acta Astronomica Sinica, Vol. 27, 368-376.
• Zheng D.W., Dong D.N. (1987) Narrow Band Filtering of Polar Motion Series Using a MultiStage Filter, Chinese Astronomy and Astophysics, Vol. 11, No. 2, 155-161.
• Zheng L.-X., Chang Q.-X. (1993) Difference Filter and its Application in Separating Periodic Components of Polar Motion, Chinese Journal of Astronomy and Astrophysics, Vol. 17, Issue 1, 107-115.
• Zheng D., Chao B.F., Zhou Y. and Yu N. (2000) Improvement of Edge Effect of the Wavelet Time-Frequency Spectrum: Application to the Length of Day Series, Journal of Geodesy, Vol. 74, No. 2, 249-254.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).