Applying Low-pass and High-pass Filters to the Original Signal

In the one-level wavelet decomposition process, the original signal undergoes low-pass and high-pass filtering respectively, followed by binary downsampling to obtain low-frequency and high-frequency coefficients (also referred to as approximation and detail coefficients). Multi-level decomposition recursively applies the same wavelet decomposition to the low-frequency coefficients obtained from the previous level, enabling hierarchical signal analysis.