Physics Letters A 317 (2003) 64–72 www.elsevier.com/locate/pla Detection of weak transitions in signal dynamics using recurrence time statistics J.B. Gao ∗ , Yinhe Cao, Lingyun Gu, J.G. Harris, J.C. Principe Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA Received 18 March 2003; received in revised form 29 July 2003; accepted 8 August 2003 Communicated by C.R. Doering Abstract Signal detection in noisy and nonstationary environments is very challenging. In this Letter, we study why the two types of recurrence times [Phys. Rev. Lett. 83 (1999) 3178] may be very useful for detecting weak transitions in signal dynamics. We particularly emphasize that the recurrence times of the second type may be more powerful in detecting transitions with very low energy. These features are illustrated by studying a number of speech signals with fricatives and plosives. We have also shown that the recurrence times of the first type, nevertheless, has the distinguished feature of being more robust to the noise level and less sensitive to the parameter change of the algorithm. Since throughout our study, we have not explored any features unique to the speech signals, the results shown here may indicate that these tools may be useful in many different applications.  2003 Elsevier B.V. All rights reserved. 1. Introduction Detection of transitional signals in noisy and non- stationary environments is both very important and challenging. Example applications include meteorol- ogy, where quantitative description of when and where the weather pattern is going to change is crucial for accurate weather forecasting; and physiology, where timely detection of transitions from a normal to abnor- mal state may help make medications more effective. Motivated by potential high pay-off in many differ- ent areas of science and engineering, this topic has at- tracted much attention recently, and a number of meth- * Corresponding author. E-mail address: gao@ece.ufl.edu (J.B. Gao). ods have been proposed using nonlinear dynamical systems theory [1–8]. Most of these methods are based on quantifying certain aspects of the nearest neighbors in phase space. Recently it has been shown [9] that the nearest neighbors in phase space can be broken down into true recurrence points and sojourn points, and two types of recurrence times can be defined. The concepts of sojourn points and two types of recurrence times greatly facilitate the quantification of recurrence plots [1,10], and it is speculated [10] that measures re- lated to these concepts may all be useful to the detec- tion of nonstationarity and state transitions in a time series. Along this line, Marwan et al. [11] have devel- oped an algorithm by quantifying the sojourn points in a recurrence plot to characterize heart rate variabil- ity. To deepen our understanding of these new con- cepts and especially to ease and motivate further ap- 0375-9601/$ – see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2003.08.018