One-Dimensional Fractional Brownian Motion Synthesis :: Using Wavelets (Wavelet Toolbox)

Wavelet Toolbox

One-Dimensional Fractional Brownian Motion Synthesis

This section takes you through the features of One-Dimensional Fractional Brownian Motion Synthesis using one of the MATLAB Wavelet Toolbox specialized tools.

For the examples in this section, switch the extension mode to symmetric padding, using the command:

```
dwtmode('sym')
```

The Wavelet Toolbox requires only one function to generate a fractional Brownian motion signal: wfbm. You'll find full information about this function in its reference page.

In this section, you'll learn how to

Generate a fractional Brownian motion signal
Look at its main properties
Save the synthesized signal

Since you can perform the generation either from the command line or using the graphical interface tools, this section has subsections covering each method.

A fractional Brownian motion (fBm) is a continuous-time Gaussian process depending on the Hurst parameter 0 < H < 1. It generalizes the ordinary Brownian motion corresponding to H = 0.5 and whose derivative is the white noise. The fBm is self-similar in distribution and the variance of the increments is given by

```
Var(fBm(t)-fBm(s)) = v |t-s|^2H
```

where v is a positive constant.

Image Fusion Using the Graphical Interface Fractional Brownian Motion Synthesis Using the Command Line