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Digital power spectral analysis and coherency analysis are powerful techniques for studying ultra-low-frequency (ULF) waves in the earth's magnetosphere. Wave polarization parameters provided by these techniques are important in the development of theoretical models for wave generation. Because of this, it is important to understand the capabilities of the digital analysis techniques. Three different techniques of using the spectral matrix to do wave analysis have been presented in the literature. Because data for wave studies involve measurement in arbitrary coordinate systems, it is necessary to transform the spectral matrix to the principal plane of the wave before coherency analysis can be performed. The fundamental differences in the three techniques lie in how they determine the transformation to the principal plane. A comparative study of these three techniques was done using simulated data involving known wave and noise properties and real ULF wave event data from the geosynchronous satellites ATS 1 and ATS 6. In general, the quality of performance of the three different techniques on both simulated and real wave events was approximately the same.