Limitations and Difficulties in Signal Processing by Means of the Principal-Components Analysis

Principal-components analysis is sometimes used in analysis of biophysical signals. Because the expansion coefficients obtained in this analysis have the property that they are uncorrelated, several authors made the extrapolation that the eigenfunctions of the covariance matrix, which also result from the principal- components analysis, correspond to independent physiological generators. By means of a theoretical example it is proved that this interpretation is unjustified because the eigenvectors are necessarily orthogonal due to the symmetry of the covariance matrix. Signals resulting from independent physiological generators do not necessarily have this property.