Finding Increment Statistics on various types of Wavelets under 1-D Fractional Brownian Motion Synthesis

Abhishek Sharma, Bhubneshwar Sharma

Abstract: This research paper demonstrates a method to analyze effect of refinement, fractal index and item state on statistical behavior of various wavelets and finally we conclude that Haar wavelet type has highest standard deviation, median absolute deviation and mean absolute deviation values in all of the wavelets that we discussed in this paper and dmey wavelet has the lowest standard deviation, mean absolute deviation and median absolute deviation values. We use value of refinement = 10, value of fractal index = 0.1, length =100 and item state =1 in each wavelet type to analyze effect on first order increment and at the same time we analyze statistical behavior of Histogram, cumulative histogram, autocorrelation and FFT (Fast Fourier Transform) energy spectrum.

Keywords: Fractional Brownian motion, Fast Fourier Transform