Detrended Fluctuation Analysis of Spatially Extended Digital Surfaces: the Classification Process of 1/f Noise and Computacional Performance

A two-dimensional Detrended Fluctuation Analysis (DFA-2D) was employed for the charactarization of 1 f classic white, pink and brownian noises.The values were compared with the fBm and fGn fractal signals.The exponent α was evaluated and compared with exponent β of the power spectrum.It was determined that the DFA-2D was capable of detecting and characterizing the different signals.In addition, the relation between α and β was defined as β ≡ 2α-2 for two-dimensional signals, with the exception of the fBm signals, where β ≡ 2α.A computational analysis of the time and accuracy of the DFA-2D was also carried out.The complexity of the method grows exponentially with the enlargement of the image size and the process becomes very slow for images greater than 1000x1000 pixels.