The capability of KL expansion to find a minimum number of independent parameters in order to describe a given statistical ensemble or database is intensively used in various theoretical and applied fields of science. The appearence of powerful and fast computers helps tackling one of thw main problem for KL application, namely the computational cost of solving the integral equation (2). For some important cases effecient algorithms like method of snapshops were developed. Other difficulties concerning the usage of KL can be illuminated by a proper choice of the averaging procedure, for instance.
The optimality of KL method alows one to reduce an amount of information about the signal or process down to a reasonable number of independent eigenfunctions, whose represent important characterictic features of the signal. Therefore, KL is a very suitable tool for the post-processing analysis.