P. G. Vaidya
MME Dept., Washington State Univ., Pullman, WA 99164
The trans-spectral coherence technique (TSC) [Vaidya and Anderson, J. Acoust. Soc. Am. 89, 2370--2378 (1991)] has been used to remove noise and distortions from periodic signals. Recent results show that the technique is also well suited to analyzing nonstationary signals, including chaos. For example, TSC can be used to distinguish a chaotic signal from a random one. As opposed to a truly random signal, in chaotic signals nonzero TSCs are required, at least for some combinations. In fact, for the Duffing equation undergoing chaos, nearly perfect trans-spectral coherence was observed for many combinations. In this case, TSC proved to be a very useful diagnostic tool, and it helped develop a deeper insight into the nature of the specific attractor, and the associated invariant group structures. Similar strong coherences have also been observed in speech signals. This sheds further light on the issues of speaker and speech recognition. Further, it is important in many fields (heart arrythmia, for example), to be able to predict in advance that a periodic system is likely to become chaotic. TSC can be used to arrive at a premonition of such a forthcoming change.