Spectral Analysis using Two-dimensional Fast Orthogonal Search (2D-FOS)

E. Abdelkawy and D. McGaughey (Canada)

Keywords

Fast orthogonal search, spectral analysis, subharmonic frequency.

Abstract

The fast orthogonal search (FOS) is a method of modelling a time-series to a weighted sum of arbitrary functions. FOS can be used for spectral analysis by fitting a functional expansion of sinusoidal functions. FOS can accurately detect subharmonic frequencies (frequencies less than one period in the record length), and high-resolution frequencies (frequencies between fast Fourier transform (FFT) frequency bins). This paper considers the extension of spectral analysis using FOS to two-dimensional (2D) data records. Trigonometric relations are exploited to compute the 2D cross-correlations of the candidate sinusoids to avoid point-by-point computation. The results of modelling a test signal show that 2D-FOS can accurately detect subharmonic and high-resolution frequencies at low signal-to-noise ( S/N ) ratios. For practical application, 2D-FOS is applied to restore a circular target in a simulated image corrupted by noise.

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