Haar Wavelet Transform

The Haar Wavelet Transform is a mathematical operation that splits a discrete signal into local averages and details. Unlike the global Fourier Transform, which uses sine and cosine waves that extend infinitely, the Haar transform uses localized basis functions, making it excellent for analyzing signals with sudden changes or identifying local features without affecting the global representation.

Experiment

In the interactive module at https://riano.app/module/haar-wavelet-transform, you can explore the Haar Wavelet Transform for different basic signal shapes.

1. Select the Ramp signal from the dropdown.
2. Switch between Level 1 and Level 2.
3. Observe how the coefficients change and how the details capture the differences between adjacent points. You can verify that the signal energy always exactly matches the coefficient energy, confirming that the transform is orthonormal and energy-preserving.