A Method for Estimating the Fractal Dimension and Filtering of Fractal Noise in Periodic Signals

S.Y. Yuen, C.K. Fong, and K.L. Chan (PRC)


Fractal dimension, Hough transform, Signal estimation


This paper considers the scenario of a periodic signal consisting of a sum of sinusoids with different unknown frequencies and phases with added fractal noise of an unknown fractal dimension. A novel method is first reported to estimate the fractal dimension. It converts the problem to a line detection problem and then apply the Hough transform. Experimental comparison with the conventional method of least square estimation is reported. The method is shown to detect the fractal dimension more accurately. Using the estimated fractal dimension, various filters are used to remove the fractal noise. It is found that an amplitude subtraction filter gives the best performance. An indicator is also suggested to estimate the likelihood that the input signal is a periodic signal superimposed on fractal noise.

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