Fluctuation and Noise Letters Vol. 0, No. 0 (2001) 000–000 c  World Scientific Publishing Company Conditions for the applicability of the Principal Component Analysis to the characterization of the 1/f -noise Jos´ e Manuel L´opez-Alonso,Javier Alda Optics Department. University Complutense of Madrid School of Optics. Av. Arcos de Jal´on s/n 28037 Madrid. Spain jmlopez@opt.ucm.es ; j.alda@fis.ucm.es Received (received date) Revised (revised date) Accepted (accepted date) 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 tem- poral 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 multi- dimensional 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. Keywords :1/f noise, principal component analysis, image arrays, noise filtering 1. Introduction The presence of 1/f -noise is ubiquous. It appears in a variety of natural and artificial phenomena in a wide range of knowledge areas (biology, ecology, economics, information systems, etc.) [1, 2]. In most of these cases the 1/f -noise appears as a collective behavior. It is usually parameterized with a single parameter given by the α exponent of the 1/f α dependence. The practical effect of the 1/f -noise is an increase of the variance of the noise with time [3]. The noise of an individual element in a collectivity may be modeled as an obser- vation of a stochastic phenomenom evolving with time. Within this approach it is possible to define a multidimensional random variable. The successive components of this multidimensional variable correspond with successive instants of time. This approach has been successfully applied to the characterization of noise in a sequence of images. The signals of the individual pixels are the observations of a multidi- mensional random variable whose components are the frames [4]. The stochastic