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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).

Figure 3.3 DWT schematic.

(3.6)

(3.7)

Here, φ_j,k(n) is the scaling function belonging to (L) and ω_j,k(n) is the wavelet function belonging to (H), M is length of signal, n is the discrete variable lies between 0 and M − 1, J = log₂(M), with k and j taking values from {0 – J − 1}. The values of A_i and D_i are computed below by Equations (3.8) and (3.9).

(3.8)

(3.9)

In previous works we have seen that theta (4–8 Hz) is preferably explored for finding judgement tasks, studying the cortical activity in left side of brain. We used 4-levels of signal decomposition by Daubechies 4 wavelet technique which results into a group of 5 wavelets coeffs where one group represent one oscillatory signal and presents Neuro-signal pattern through D1–D4 and A4. They have “5 frequency bands—(1–4 Hz), (4–8 Hz), (8–13 Hz), (13–22 Hz) and (32–100 Hz)”.