Using a redundant discrete wavelet transform for characterizing self-similar data sets

The wavelet transform is a very useful tool for analyzing signals with self-similar behavior by virtue of the fact that the wavelet basis itself displays self similar properties. Recordings of mean arterial pressure in conscious dogs that had been shown to exhibit nonlinear deterministic behaviour (self-similar characteristics) were used for analysis. We applied a redundant wavelet transform to these data sets and calculated the wavelet Fano factor across different scales to extract the power law exponent. Our results indicate that the redundant wavelet transform would be a useful tool in real-time analysis of data with self-similar properties.