Figure 2

Wavelet decomposition tree. MRA allows for the decomposition of a signal into several resolution levels. First, the original signal (with a power of two points) is decomposed by two complementary half-band filters (high-pass and low-pass filters) that divide a spectrum into high-frequency (detail coefficients; D₁) and low-frequency (approximation coefficients; A₁) components (bands). For example, the low-pass filter will remove all half-band highest frequencies. Information from only the low frequency band (A₁), with a half number of points, will be filtered in the second decomposition level. The A₂ outcome will be filtered again for further decomposition.