Random noise reduction capability of the hermit polynomial based Least Squares Fourier Transform method

Vass, P. (2012) Random noise reduction capability of the hermit polynomial based Least Squares Fourier Transform method. Acta Geodaetica et Geophysica Hungarica, 47 (3). pp. 328-343. ISSN 1217-8977

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Abstract

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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