Wavelet transform modulus maxima method

The wavelet transform modulus maxima (WTMM) is a method for detecting the fractal dimension of a signal.

More than this, the WTMM is capable of partitioning the time and scale domain of a signal into fractal dimension regions, and the method is sometimes referred to as a "mathematical microscope" due to its ability to inspect the multi-scale dimensional characteristics of a signal and possibly inform about the sources of these characteristics.

The WTMM method uses continuous wavelet transform rather than Fourier transforms to detect singularities singularity – that is discontinuities, areas in the signal that are not continuous at a particular derivative.

In particular, this method is useful when analyzing multifractal signals, that is, signals having multiple fractal dimensions.

Consider a signal that can be represented by the following equation:

where ${\displaystyle t}$ is close to ${\displaystyle t_{i}}$ and ${\displaystyle h_{i}}$ is a non-integer quantifying the local singularity. (Compare this to a Taylor series, where in practice only a limited number of low-order terms are used to approximate a continuous function.)

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