Non Linear Techniques for Studying Complex Systems

Abstract

This chapter deals with the various techniques associated with the analysis of self similar structures of music signals as well as bio-signals obtained from EEG data. This chapter is basically a detailed analysis on the following tools of complex data analysis which have been elaborated later in the different studies. 1. Wavelet analysis 2. Detrended fluctuation analysis (DFA) 3. Multifractal detrended fluctuation analysis (MFDFA) 4. Multifractal cross correlation analysis (MFDXA) All these techniques make use of Fractal Dimension (FD) or multifractal spectral width (obtained as an output of the MFDFA technique) as an important parameter with which the emotional arousal corresponding to a certain cognitive task (in this case a particular music clip) can be quantified. MFDXA can prove to be an important tool with which the degree of cross correlation between two non-linear EEG signals originating from different lobes of brain can be accurately measured during higher order cognitive tasks. With this, we can have a quantitative assessment of how the different lobes are cross-correlated during higher order thinking tasks or during the perception of audio or any other stimuli. MFDXA can also prove to be an amazing tool in music signal analysis, where we can estimate the degree of cross-correlation between two non-linear self-similar musical clips. A higher degree of cross-correlation would imply that both the signals are very much similar in certain aspects. This in turn can be used as an important tool to obtain a cue for improvisation in musical performances as well as in the identification of presence of Ragas in songs. Several other tools for EEG feature extraction have also been discussed in detail here which include novel methods like neural jitter-shimmer as well as extraction of pitch of EEG signals.