Journal of Theoretical Medicine
Volume 3 (2001), Issue 4, Pages 231-245

Testing for Periodicity in Signals: An Application to Detect Partial Upper Airway Obstruction during Sleep

1Department of Mathematical Sciences, University of Turku, and Turku Centre for Computer Science TUCS, FIN-20014, Turku, Finland
2Department of Physiology, University of Turku, Turku, Finland

Received 24 October 2000; Revised 23 April 2001; Accepted 23 April 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A simple method for detecting periodic components of unknown periodicity in a signal is presented. The method is based on spectral decomposition of signal using orthonormal functions. Traditionally, hypothesis testing together with harmonic functions is used, but we show that the same statistical properties are obtained for other systems of orthonormal functions as well. The appropriate behavior of the method is first demonstrated with simulation studies and then tested to identify visually determined clusters of high-frequency movements, which may repeat in synchrony with respiration during sleep. The good performance in the practical tests suggests that an automatic identification of these clusters could be based on Walsh functions.