Wavelet analysis is applied to analyze polar motion spanning the years 1890--1997. First, the wavelet transform is used to identify the components (prograde and retrograde) present in the data. This wavelet transform is subsequently used to filter and reconstruct each component. Then we define the ridge of the wavelet transform and show how it can be used to detect rapid phase jumps in a signal. This technique is applied to the reconstructed prograde Chandler wobble component, and several features characteristic of phase jumps are identified. Synthetic signals with adjustable phase jumps (in terms of their dates, durations, and amplitudes) are constructed to produce ridge functions similar to the one obtained for the Chandler wobble. We find that less than 10 phase jumps are necessary to reproduce the observed features. All but one phase jump have durations between 1 and 2 years, and their dates are found to remarkably follow those of geomagnetic jerks with a delay not exceeding 3 years. Elementary statistical tests assign a high probability to the correlation between the dates of the phase jumps and those of the jerks. Simple physical models of core-mantle coupling show that the observed phase jumps can be recovered with torques of about 1020 Nm. ¿ 1998 American Geophysical Union