Wavelet transform modulus maxima method: Difference between revisions

Revision as of 17:05, 20 April 2011

Revision as of 17:05, 20 April 2011

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: <math>f(t) = a_0 + a_1 (t - t_i) + a_2(t - t_i)^2 + \cdots + a_h(t - t_i)^{h_i} \, </math>

where <math> t </math> is close to <math> t_i </math> and <math> h_i </math> is a non-integer quantifying the local singularity. (Compare this to a [[Taylor_seriesTaylor series]], where in practice only a limited number of low-order terms are used to approximate a continuous function.)

Generally, a [[continuous wavelet transform]] decomposes a signal as a function of time, rather than assuming the signal is stationary (For example, the Fourier transform). Any continuous wavelet can be used, though the first derivative of the [[Gaussian distribution]] and the [[Mexican_hat_waveletMexican hat wavelet]] (2nd derivative of Gaussian) are common. Choice of wavelet may depend on characteristics of the signal being investigated.

Below we see one possible wavelet basis given by the first derivative of the Gaussian: