Wavelet - Wikipedia

Abstraction: Time-frequency localized oscillation for signal decomposition and compression

Key points:

• Wavelets are brief oscillations with zero mean; localized in both time and frequency, unlike Fourier transforms which are only frequency-localized
• Discrete wavelet transform runs in O(N), faster than FFT O(N log N), due to logarithmic frequency division
• Multiresolution analysis (Mallat 1989) constructs orthonormal wavelet bases via father (scaling) and mother (wavelet) functions; basis of fast wavelet transform
• Daubechies orthogonal wavelets with compact support (1988) are the canonical family; Haar wavelet (1909) is the simplest
• JPEG 2000 uses DWT (CDF 9/7 wavelet for lossy, LGT 5/3 for lossless compression); standard for digital cinema since 2004
• Wavelet shrinkage (thresholding coefficients) enables effective signal denoising by exploiting sparsity in wavelet domain

Connections: Wavelets · Signal Processing · Multiresolution Analysis

Source: http://en.wikipedia.org/wiki/Wavelet