Wavelet transform

A signal transform that represents data using waveforms localized in both position and scale. It reveals when and at what scale features occur, unlike the global frequency representation of the Fourier transform.

Continuous wavelet transform: A transform that correlates a signal with continuously scaled and shifted copies of a mother wavelet. It produces a continuous map of signal features across position and scale.
Fourier transform: A transform that represents a signal as a combination of sinusoidal frequencies. Its global frequency basis contrasts with wavelets' localization in position and scale.
JPEG 2000: An image coding standard that uses wavelet transforms for multiresolution compression. Its image-coding pipeline uses wavelet coefficients to support efficient compression and scalable decoding.
Short-time Fourier transform: A time-frequency transform that applies the Fourier transform within fixed-length sliding windows. Its fixed window gives uniform resolution, unlike wavelets' scale-dependent resolution.
Alfred Haar: A Hungarian mathematician who introduced the Haar system of orthogonal step functions in 1909. The Haar system is an early wavelet basis and a direct ancestor of the discrete transform.
Discrete wavelet transform: A wavelet transform using discrete scale and position steps, often implemented with filter banks. Its sampled scales and shifts yield a compact, efficient coefficient representation.
Time-frequency analysis: Methods that describe how a signal's frequency content varies over time. Wavelet transforms are one approach to this broader analysis problem.
Wavelet denoising: A noise-reduction method that thresholds wavelet coefficients before reconstructing a signal. Localized coefficients let denoising suppress small noise contributions while retaining sharp features.
Empirical mode decomposition: An adaptive method that decomposes a signal into oscillatory components derived from its data. It builds components from the signal itself rather than selecting a wavelet family in advance.
Jean Morlet: A French geophysicist who developed wavelet analysis for seismic signal interpretation in the early 1980s. His work helped establish wavelets as a practical tool for analyzing localized seismic features.

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