Author: P. Vass 1
View More View Less
  • 1 University of Miskolc Department of Geophysics H-3515 Miskolc-Egyetemváros Hungary
Restricted access

Treating the Fourier transform as an over-determined inverse problem is a new conception for determining the frequency spectrum of a signal. The concept enables us to implement several algorithms depending on the applied inversion tool. One of these algorithms is the Hermit polynomial based Least Squares Fourier Transform (H-LSQ-FT). The H-LSQ-FT is suitable for reducing the influence of random noise. The aim of the investigation presented in the paper was to study the noise reduction capability of the H-LSQ-FT in some circumstances. Four wavelet-like signals with different properties were selected for testing the method. Examinations were completed on noiseless and noisy signals. The H-LSQ-FT provided the best noise reduction for the noisy signal having low peak frequency and wide band width. Finally, the results obtained by the H-LSQ-FT were compared to those of other traditional methods. It is showed that the H-LSQ-FT yields better noise filtering than these methods do.

  • Brigham E O 1974: The Fast Fourier Transform. Prentice-Hall Inc., Englewood Cliffs, New Jersey

    Brigham E. O. , '', in The Fast Fourier Transform , (1974 ) -.

  • Dobróka M, Szabó N 2011: Acta Geophysica, 59, 907–934.

    Szabó N. , '' (2011 ) 59 Acta Geophysica : 907 -934.

  • Dobróka M, Völgyesi L 2008: Mathematical Geoscience, 40, 299–311.

    Völgyesi L. , '' (2008 ) 40 Mathematical Geoscience : 299 -311.

  • Gröbner W, Hofreiter N 1958: Integraltafel zweiter Teil, Bestimmte Integrale. Springer-Verlag Wien und Innsbruck

  • Gyulai Á, Ormos T 1999: J. Appl. Geophys., 41, 1–17.

    Ormos T. , '' (1999 ) 41 J. Appl. Geophys. : 1 -17.

  • Gyulai Á, Ormos T, Dobroka M 2010: J. Appl. Geophys., 72, 232–241.

    Dobroka M. , '' (2010 ) 72 J. Appl. Geophys. : 232 -241.

  • Kis M 2002: J. Appl. Geophys., 50, 401–416.

    Kis M. , '' (2002 ) 50 J. Appl. Geophys. : 401 -416.

  • Menke W 1984: Geophysical Data Analysis, Discrete Inverse Theory. Academic Press Inc.

  • Szabó N P 2004: Geoph. Transactions, Vol. 44. Nos 3–4, 313–329.

    Szabó N. P. , '' (2004 ) 44. Geoph. Transactions : 313 -329.

  • Turai E, Dobróka M 2011: Acta Geod. Geoph. Hung., 46, 283–290.

    Dobróka M. , '' (2011 ) 46 Acta Geod. Geoph. Hung. : 283 -290.

  • Vass P, Dobróka M 2009: Robust Fourier Transform Algorithm Using Inversion Tools. 15th European Meeting of Environmental and Engineering Geophysics, Dublin, Ireland