Optimal Representation of Signals to be Transmitted

The problem of optimal (in terms of minimum root-mean-square error) representation of signals in the finite-dimensional basis has been solved by determining the orthogonality weight of the basis functions. Basis functions are represented by minimum-phase equidistant functions having amplitude spectrum equal to the amplitude-frequency characteristic of communication channel accurate to the constant factor. Deterministic signals can be optimally described by a few different bases each having weight function being dependent on types of signals transmitted and basis functions. There is only one way in order to determine the basis for optimal definition of the random signal, with the weight function being dependent on the basis functions and signal covariance