2.1.1. Continuous Wavelet Transform

The wavelet transform is extensively employed for ECG signal processing due to its capability to analyze non-stationary signals. The WT involves breaking down the signal into a collection of functions derived from a single function referred to as the mother wavelet, achieved through dilations, contractions (scaling) and time shifts of this function [20]. The CWT entails convolving a signal x(t) with a wavelet function ψ(t) that is translated in time by a parameter b and scaled by a parameter a. The mathematical representation is as follows:

One drawback of the implementation of the CWT is that the parameters a and b are usually discretized, and the analysis is restricted to scales that are powers of two obtaining the dyadic wavelet transform that can be computed with Mallat’s algorithm [20]. Because of this limitation, the implementation of CWT with splines allows a finer discretization of the CWT at the integers a y b so that it can handle more scales [21].