This paper presents results on the multiresolution analysis of nonstationary signals with the objective of detecting underlying periodic phenomena. Wavelet packet analysis with coefficient thresholding is the basis for the detection. The effectiveness of the method is illustrated by analyzing experimental data on sediment electrochemical redox potential in a tidal microcosm. The significance of the technique is that it can extract periodic phenomena from experimental data corrupted by catastrophic and random events, provide a signature of the basic periodic component, an give an estimate of the degree of deviation from periodic behavior. Consequently, it has potential applications in the analysis of quasi-periodic signals such as electrocardiograms (ECGs), where the determination of the extent of quasi-periodicity is of critical importance.