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.
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Brigham E. O., '', in The Fast Fourier Transform, (1974) -.
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Dobróka M, Szabó N 2011: Acta Geophysica, 59, 907–934.
Szabó N., '' (2011) 59Acta Geophysica: 907-934.
Szabó N.Acta Geophysica201159907934)| false
Dobróka M, Völgyesi L 2008: Mathematical Geoscience, 40, 299–311.