IEVref: 103-04-11 ID: Language: en Status: Standard Term: wavelet Synonym1: Synonym2: Synonym3: Symbol: Definition: small localized wave, represented by a function having a zero mean value and a practically finite durationNote 1 to entry: From a mother wavelet $\psi \left(t\right)$, daughter wavelets are obtained through shifting and scaling (expansion or compression): ${\psi }_{a,b}\left(t\right)=\frac{1}{\sqrt{a}}\psi \left(\frac{t-b}{a}\right)$, where a is a scale parameter and b a position parameter. Note 2 to entry: Examples (see Figures 3 and 4): Haar wavelet: $\psi \left(t\right)=-1$ for −1/2 < t < 0, $\psi \left(t\right)=1$ for 0 < t < 1/2, $\psi \left(t\right)=0$ outside; Morlet wavelet: $\psi \left(t\right)={\mathrm{e}}^{-{t}^{2}/2}{\mathrm{e}}^{-\mathrm{j}\omega \text{ }t}$ (example of exponential damping; Figure 4 gives the real part). Figure 3 – Haar waveletFigure 3 – Ondelette de Haar Figure 4 – Morlet wavelet Figure 4 – Ondelette de Morlet Publication date: 2009-12 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO 2017-08-25: Added a tag. LMO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: