Kaiser window efficiency in calculating the exact fractal dimension by the power spectrum method

Abstract

Exact fractals are a type of self-similar fractals with a special form of self-affine fractals. Recently, algorithms have been developed to calculate the dimension of such fractals by the box-counting method. In this article, exact fractals will be investigated using the power spectrum method and wavelets. In the used algorithms, we use Daubechies and Symlet wavelets of orders 3 to 8 and show the efficiency of the Kaiser window function in the more accurate calculation of the exact fractal dimension. The comparison of the results obtained by the box-counting method on two types of accurate fractals that have been investigated recently shows that the power spectrum and wavelet method using the Kaiser window filter has higher accuracy.