Cognitive Scaffold

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MENTAL MODEL · M6035

Wavelet Transform

Wavelet Transform
TechnicalHigh supportComputer Science
Included
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Version 1.0.0 · Updated 2026-07-28

CORE DEFINITION

Wavelet analysis or wavelet transform refers to representing a signal using the oscillatory waveforms of a finite-length or rapidly decaying "mother wavelet". The waveform is scaled and translated to match the input signal. The term "wavelet" was coined by French scholars Jean Morlet and Alex Grossmann in the early 1980s. They used the French word "ondelette", meaning "small wave". Later, in English, "onde" was changed to "wave" to form "wavelet". The development of wavelet transform inherits the localization idea of Gabor transform and overcomes some defects of Fourier and Gabor transforms. Wavelet transform provides an adjustable time-frequency window whose width changes with frequency: as frequency increases, the time window narrows to improve resolution. The wavelet has an average amplitude of zero over the entire time range, has finite duration, and can have abrupt changes in frequency and amplitude, and can be irregular or asymmetric.

SCAFFOLDING EFFECT

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Reduce cognitive load

Wavelet analysis or wavelet transform refers to representing a signal using the oscillatory waveforms of a finite-length or rapidly decaying "mother wavelet". The waveform is scaled and translated to match the input signal. The term "wavelet" was coined by French scholars Jean Morlet and Alex Grossmann in the early 1980s. They used the French word "ondelette", meaning "small wave".

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A mathematical tool that uses scalable and translatable "wavelet" basis functions to analyze signals, capturing local features at different scales, with both time and frequency resolution.

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Source support: Explicit

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