A wavelet is a localized function whose translates and dilates analyze different positions and scales.
A multiresolution analysis is a nested sequence of approximation spaces related by dyadic dilation and generated at one scale by translates of a scaling function.
The Meyer-Mallat theorem associates an orthonormal wavelet basis to every orthonormal multiresolution analysis.
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A wavelet is a mathematical function used to divide data into different frequency components and study each component with a resolution that matches its scale. It is particularly useful for analyzing non-stationary signals, which can change over time, unlike traditional Fourier transformations that analyze signals in a fixed manner.