The Information Rate for Continuous-Parameter Stationary Gaussian Random Processes I
Ken-ihi Yoshihara · Institutional Repositories DataBase (IRDB) · 1969
In [3], various definitions of information rate for the stationary processes are introduced and the interrelationships among them are considered. Especially, there are explicit formulas which enable one to compute the information rate of stationary Gaussian process with some conditions. We shall derive the same formulas under less restrictive conditions. The paper is presented in three parts: the first, appearing here, treats the preliminary results (Theorems 1 and 2) concerning the information rate of one-dimensional continuous-parameter stationary Gaussian processes ; the second gives the general condition which satisfies the conditions of the above theorems ; the third will treat the information rate of multi-dimensional regular stationary Gaussian processes of, not necessarily, maximum rank. The author is indebted to Professor M. Udagawa of Tokyo University of Education for many valuable comments.