AbstractThe theoretical limit of data compression concerning an analog source is given by Kolmogorov's ϵ‐entropy. But in practical systems in which analog signals are transmitted digitally the sampling and quantizing processes are indispensable. In this paper the ϵ‐entropy of the band‐limited stationary Gaussian signal is obtained and it is shown by use of sampling theorem that it has the same value as in the case of a uniformly sampled signal (stationary Gaussian series). By adding the error due to band‐limiting (sampling error) and the redundancy residue to the quantizing to the ϵ‐entropy and under the restrictions of sampling and quantizing, the relation between mean‐square‐error and transmission rate (speed) can be formulated. By adjusting sampling and quantizing intervals, the data compression limits to such a sys