**1. Introduction**

Depression refers to a state of mental disorder accompanied by mood variations that affect the thought process, social and physical well-being of an individual. World Health Organisation reports that more than 264 million people under all age group suffer globally from this leading cause of disability. Depression may also

sometimes lead to cognitive impairment. History demonstrates that depressive disorders have been with human civilization from the very beginning of the mankind. Unlike many other ailments that affect the health of an individual, an early diagnosis of this mental disorder is highly challenging. Timely medical intervention has been proved to be very effective in arresting the progression of this disorder. Automated diagnosis using EEG signals of the brain would be highly beneficial in the effective clinical intervention and thereby assisting the psychiatrists in the assessment of mental state.

EEG signals contain information about the state of the brain. The variations in the biosignals, indicating certain symptoms, are highly subjective and may appear at random in time scale. The electroencephalogram has been used as a tool for investigating the brain electrical activity in different physiological and pathological states for several decades. The identification of neurophysiological events, different behavioural states and the localisation of the areas involved constitute a relevant task in the EEG analysis.

Electroencephalogram (EEG) is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. It is a tool which helps in diagnosing various disorders of the brain and also helps in studying the functional state of the brain. EEG recording is most commonly done by placing the electrodes on the scalp while localised measurement of potentials is done subdurally or from the cerebral cortex. Electrode placement for recording EEG is based on the International 10–20 electrode placement system. The amplitude of the EEG signal is slightly less than 10 μV to slightly more than 100 μV p–p and the frequency ranges from 0 to slightly greater than 100 Hz. Earlier, the analysis of EEG has been based on the assumption that the EEG signals are generated by a highly complex linear system, but later they have been interpreted as the output of a deterministic system of relatively low complexity but containing nonlinear elements. Thus applying the concept of deterministic chaos to the EEG, it can be characterised by various parameters [1]. EEG studies of depression patients have been proven worthwhile for quantitative analysis that will lead to the development of automated clinical diagnostic tools.

In this chapter we discuss the method to characterise and compare frontopolartemporal EEG signals of depression patients and normal controls using signal processing and nonlinear methods. An 8-level Multiresolution decomposition of the time -frequency analysis, which decomposes a mixed signal into signals at different frequency bands, is attempted. Energy at different resolution levels has been calculated using Parseval's theorem. Relative Wavelet Energy (RWE) is used to characterise the EEG signal energy distribution of healthy subjects and depression patients at different frequency bands. Wavelet Entropy calculations are performed to assess the degree of order associated with the acquired signals. All the aforementioned measures posit better quantitative measures in the comparative study of brain activity and complexity in depression patients and normal controls.
