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Signal processing is the process of modelling, detection, identification and utilization of patterns and structures in a signal. Random signals are processed through statistical models of signal processing, which are used for decision making systems, extracting the relevant information from noisy, distorted and incomplete signals. A signal describes the information through variation of quantity which reflects the properties, characteristics, state, the course of action and the information about a source and that information may be processed directly by humans or machines for the purpose of decision, forecasting, control, investigation, research and further exploration of an object [48].

Biomedical signal processing centres on the acquisition of vital signals extracted from biological and physiological systems. These signals help us to obtain information about the current state of living systems, and therefore, their monitoring and interpretation have significant diagnostic value for clinicians as well for researchers to extract information related to human health and diseases.

Biomedical signal processing depends on the knowledge of their origin, nature of the signals, their properties and their complexities which come along signals. They have to be clearly examined to be processed non-invasively and indirectly due to their underling complex biological structure. In addition, the extracted signals are not always ready to be used because of noise. These unwanted signals are sometimes due to malfunctioning of the equipment or sometimes due to other body signals that create a hindrance in obtaining the required results.

Consequently, pre-processing of the signals is required to get the required set of data for further experiments.

This section briefly introduces the signals we have used for our research work, i.e., gait and EEG signals. It also provides information about feature extraction and feature selection techniques and also explains feature classification.

2.4.1 Gait and EEG Signals

A cyclic movement of the feet in which one or the other alternate strikes to ground is called gait [49], and the measures obtained by the stride-to-stride movements of the feet are called gait signals [50]. Hausdorff et al in [50] suggested that the understanding of the relationship between loss of motor neurons and the perturbation in the stability of stride-to-stride dynamics can help us to monitor neurodegenerative diseases progression and in assessing potential therapeutic interventions. Gait cycle duration is also referred as the stride time, i.e., fluctuation from one stride to the next in a complex manner. Due to intact neuronal control the fluctuation magnitude of the strides in control subjects is relatively small (~2%).

A variation of the surface potential on the scalp reflects the functional activity of the brain. This surface potential of the brain is collected by electrodes, attached on the scalp. The voltage between the electrodes is measured and ultimately this is filtered, amplified and the recorded data is collected, which commonly is known as EEG. EEGs are used as a method of investigating mental processes to investigate any perturbation in the brain activity. The EEG is roughly defined as the mean electrical activity in the brain at different sites of the head [51]. More specifically, it can be defined as the extracellular current flows of a large number of neurons.

2.4.2 Feature Extraction and Feature Selection

The pattern recognition process consists of two steps; feature extraction and feature classification. A feature is one particular aspect of an instance that can assist in grouping it to a particular class. In other words, features are synonymous of input variables or the attributes of a dataset that provide good representation of a specific domain, related to the available

measurements [52]. In the case of medical diagnosis, these features can be the symptoms of a disease. The features can be qualitative or quantitative as shown in the Figure 2-3.

Figure 2-3: Types of Features [53]

Feature extraction consists of finding a set of measurements or block of information to present the properties of the signal [54]. These features are the basic index of detection, classification and regression in the field of biomedical signal processing and also in data analysis.

The expression of the features can be binary, categorical or continuous. For instance, they can be the physical condition of the patient (age, health status, family history), position of the electrode on the scalp to get EEG signals, or may be EEG signal descriptor (frequency, voltage, amplitude, phase, etc.) [54]. The performance of the pattern recognition system depends on the features we select and also on the classification algorithms.

This process also removes erroneously recorded signals caused by sensor malfunctioning and noise that can have a negative effect on signal classification. This process can be defined using the following mathematical formula and the process is illustrated in Figure 2-4.

Where I(t) is the data retrieved from the data source, that is mapped to some signal S(t) and the inherited noise found in the signal is defined as N(t). Consequently, the filtered value can be defined as the signal S(t) - the noise value N(t).

Source of Information Information to Signal Mapping Communication Channel

Digital Signal Processing Processor Filtered Signal Signal Signal Noisy Useful Information

Figure 2-4: Feature Extraction and Noise Reduction Process

Feature selection, on the other hand, is the process of identification and removal of irrelevant as well as redundant features from the datasets [55]. The existing datasets may have hundreds and thousands of features. Some of them could be totally irrelevant or some others may have redundant information. This can lead to more complications and also to the increased processing time of classification. This is also effective in handle multi-dimensional data, which ultimately enables data mining algorithms to work more efficiently and effectively. Different methods are available to handle this issue. More details are available in [55].