Contribution to the Berkner scheme for the approximation of the continuous wavelet transform: application to the measure of the latency time of the genioglossus muscle. (Contribution au schéma hiérarchique de Berkner pour l’approximation de la transformée en ondelettes: application à la mesure électromyographique du temps de latence du muscle génioglosse.) (French) Zbl 1059.94510
Summary: The continuous wavelet transform is widely used in signal processing. It enables one to choose significant scales with respect to detection and localization purposes. The Berkner transform is an approximation of the continuous wavelet transform, for which we propose an original synthesis formula. We then build a detector of reflex activity in EMG signals using the Berkner transform. The significant scales are determined through the use of the reconstruction formula. The electromyographic measurement of the reflex activity of the genioglossus muscle under stimulation is of great interest for the study of sleep apnea. The reflex activity is a complex mixture of unpredictable nonstationary events that are superimposed on a stationary background containing noisy transients. The detector of reflex activity we propose is both robust and accurate. We end the paper with a statistical analysis of the detector performances on synthetic signals, and we give an illustration of the method on real signals.
MSC:
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 94A13 | Detection theory in information and communication theory |
| 92C55 | Biomedical imaging and signal processing |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 65T60 | Numerical methods for wavelets |
| 62B10 | Statistical aspects of information-theoretic topics |
