Understand signal decomposition and reconstruction through visualization.
Using the Haar Wavelet: \( h = [0.5, 0.5] \) (Low-pass) and \( g = [0.5, -0.5] \) (High-pass).
Low-frequency: Captures the "trend".
High-frequency: Captures "edges" or "noise".
Try silencing the Detail coefficients. In JPEG2000 or audio compression, small detail values are often set to zero to save space.
Mathematically: \( x[n] = \text{upsample}(A) * h_{inv} + \text{upsample}(D) * g_{inv} \)