Local spectral analysis using wavelet packets

Wavelet packets are a useful extension of wavelets, which are of wide potential use in a statistical context. In this paper, an approach to the local spectral analysis of a stationary time series based on wavelet packet decomposition is developed. This involves extensions to the wavelet context of standard time series ideas such as the periodogram and spectrum. Some asymptotic properties of the new estimate are provided. The technique is illustrated by simulated signals and its application to physiological data, and its potential use in studies of time-dependent spectral analysis is discussed.