wavelet-creation

We present a novel technique for the calculation of the coefficients required for a Wavelet Multiresolution Analysis (WMA). When a WMA is performed, a mother wavelet is used as a decomposition base to find how the scales and translations of the wavelet best describe the signal. The result of decomposition is a matrix containing the weight for each scale and time instant. To perform the decomposition, a filter bank composed with a low pass filter build with the scaling coefficients and a high pass filter build with the wavelet coefficients it is used. By reconstructing using a selected subset of the scales, we can use the WMA to reduce noise. Our proposal focuses on finding the scaling and wavelet coefficients that best describe a given function by solving an optimization problem with nonlinear restrictions. As an example of the proposed model, we create a new wavelet using as a function the base of communication between neurons, the Spike. With the calculated coefficients, we use the WMA to demonstrate the reduction of noise from a set of brain signals related to visual stimuli.