Analysis of a wavelet arising from a model for arm movements during epileptic seizures, ProRISC Workshop, Veldhoven, The Netherlands, 29-30 november 2007

This paper analyses a wavelet that arises in the study of myoclonic seizures. The wavelet comes about when a physiological model is used that describes arm movements associated with certain epileptic (myoclonic) seizures. Due to the simple analytical form of the wavelet, x(t) = 0 for t <0 and x(t)=te¡t ¡ tA e ¡t B for t ¸0, with B2 tAt1, explicit omputations are feasible for the frequency response X(w), the admissibility condition and admissibility constant, the wavelet transform of x itself using x or its time-reversed version x¡ (matched filter) as analyzing wavelet, etc. The new wavelet is expected to yield better detectability for the problem at hand than general purpose wavelets would do. We show one example of how the new wavelet performs on clinical data and we intend to follow up this study with a more elaborate demonstration of its efficacy. The new wavelet, and some of its variants (such as the odd extension of it and a Gaussian smoothed version of it), are briefly compared with certain wavelets presented in existing literature. Our preliminary conclusion, to be elaborated in the near future, is that the wavelet has excellent potential in the detection of myoclonic seizures from accelerometric data of arm movements of epileptic patients.