Multi-resolution analysis - see both time and frequency
Fourier: Perfect frequency resolution, no time localization. A short burst looks the same as a continuous tone in the spectrum.
Wavelets: Trade-off between time and frequency resolution at each scale. Short events are localized in time AND frequency.
Decomposition: Low-pass filter → Approximation (A), High-pass filter → Detail (D). Repeat on A for multi-level analysis.
Applications: Image compression (JPEG2000), denoising, feature detection, ECG analysis.