Sharp increase of the Alfv¿n speed above the ionosphere is expected to create a resonant cavity for the Alfv¿n waves traveling along the geomagnetic field lines (so-called Ionospheric Alfv¿n Resonator). The wavelet transform has been used to analyze magnetic and electric fields recorded on Freja satellite. Cross-phase spectra between field components in the frequency range 0.5--10 Hz reveal a pattern similar to that predicted theoretically for the resonator. The Fourier cross-phase spectra fail to show any characteristic features. We conclude that this is due to the spatial structure of the resonator which can be examined only with local analysis techniques. ¿ 2000 American Geophysical Union