The transmission of analog information over digital communications channels

Methods for synthesizing instruments and systems for this type of transmission that are optimal with respect to a minimum rms error are discussed. Equations for quantization and evaluation are given for different versions of these systems. The principles underlying the theory of epsilon-entropy in relation to scalar and vector quantities and processes and to the two-variable function are discussed. Attention is also given to aspects of the quantization and digital representation of analog random quantities and processes. Nonlinear and linear filters of scalar and vector analog messages in a communications system with pulse-code modulation are synthesized, as are different versions of the communications system with differential pulse-code modulation for scalar and vector messages. Also synthesized are different versions of the two-variable function and stationary and nonstationary (adapting to changes in dispersion and spectral density) messages for channels with errors and channels without errors.