Automatic nonlinear modeling of multiperiodic biomedical variables with unequidistant sampling

Estimation of multiple frequencies In biomedical variables with unequidistant sampling is not a straightforward issue. The use of sinusoidal models can lead to misleading results and the methods based on a model of multiple sinusoidal components present several problems. These methods are usually based on trying different combinations of frequencies to look for the best model. In the current linear algorithms, the trial frequencies must be chosen a priori. A trade-off solution must be adopted, because with a high number of frequencies the candidates are close to the spectral peaks, but the probability of detection is low for a fixed probability of false detection. In practice it is not possible to know a priori which is the best set of trial frequencies. On the other hand, the multiple tests problem that arises when multiple frequencies are statistically checked is often ignored. We propose a new nonlinear procedure to estimate automatically a model of multiple sinusoidal components that overrides these problems. This procedure uses nonlinear regression to choose directly the spectral peaks as trial frequencies, increasing in this way the probability of detecting a true component. On the other hand, the problem of multiple tests is managed with a simple statistical technique.