Conditions for the applicability of the principal component analysis to the characterization of the 1/f-noise

Principal Component Analysis (PCA) has been applied to the characterization of the 1/f-noise. The application of the PCA to the 1/f noise requires the definition of a stochastic multidimensional variable. The components of this variable describe the temporal evolution of the phenomena sampled at regular time intervals. In this paper we analyze the conditions about the number of observations and the dimension of the multidimensional random variable necessary to use the PCA method in a sound manner. We have tested the obtained conditions for simulated and experimental data sets obtained from imaging optical systems. The results can be extended to other fields where this kind of noise is relevant.