LITMIR.BIZ

Figure 3.2 Workflow diagram.

      3.4.1 Pre-Processing & Feature Extraction

      We shall discuss how we used S-Golay filter to even out the signals and then DWT based wave-let analysis to extract features from Neuro-signals.

       3.4.1.1 Savitzky–Golay Filter

In layman words [24] if we try to understand this filter, it is a polynomial based filter in which least square polynomial method find out the filtered signals with combinedly evaluating the neighbor signals. It can be computed for a signal such as S_j = f(t_j), (j = 1, 2, …, n) by following Equation (3.3).

(3.3)

Here, ‘m’ is frame span, c_i is no. of convolution coeffs. and Q is the resultant signal. ‘m’ is used to calculate instances of c_i with a polynomial. In our case, this was used to smoothen Neuro-signals by a frame size of 5 with a polynomial of degree 4.

       3.4.1.2 Discrete Wavelet Transform

In layman words, it is used to convert incoming signal into sequences of smaller waves using multi-stage decomposition. This enables us to analyze multiple oscillatory signals in an approximation and detail coefficient form. Figure 3.3 has shown the decomposing structural of brain neuron signals when it is preprocessed using low & high filtering methods. Low filter pass method (L) removes high voltage fluctuations and saves slow trends. These in turn provide approximation (A) of the signal. High pass filter method (H) eliminates the slow trends and saves the high voltage fluctuations. The resultant of (H) provides us with detail coefficient (D) which is also known as Wavelet coefficient. The Wavelet function is shown in Equations (3.4) and (3.5).

(3.4)

(3.5)

Here ‘a’ and ‘b’ are scaling parameter and translation parameter containing discrete values. ‘m’ is frequency and ‘n’ is time belonging to Z. The computation of (A) and (D) is shown in scaling function (3.6) and wavelet function (3.7).