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IEVref: | 103-04-12 | ID: | |

Language: | en | Status: Standard | |

Term: | continuous wavelet transform | ||

Synonym1: | CWT | ||

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Definition: | integral of the product of a function and a shifted and scaled wavelet Note 1 to entry: For a function $f(t)$ and a wavelet $\psi (t)$: ${C}_{f}(a,b)={\displaystyle {\int}_{-\infty}^{+\infty}f(t)}\text{\hspace{0.17em}}{\psi}_{a,b}^{\ast}(t)\mathrm{d}t$ where Note 2 to entry: A discrete wavelet transform is obtained by choosing a finite number of values of the two parameters. The inverse transform expresses the function of time as a superposition of wavelets. | ||

Publication date: | 2009-12 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO | ||

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Note 1 to entry: For a function $f(t)$ and a wavelet $\psi (t)$:

${C}_{f}(a,b)={\displaystyle {\int}_{-\infty}^{+\infty}f(t)}\text{\hspace{0.17em}}{\psi}_{a,b}^{\ast}(t)\mathrm{d}t$

where *a* is the scale parameter, *b* is the position parameter, and * denotes the complex conjugate.

Note 2 to entry: A discrete wavelet transform is obtained by choosing a finite number of values of the two parameters. The inverse transform expresses the function of time as a superposition of wavelets.