The study course is intended to deepen their knowledge of signal sampling and approximation, of linear system theory based on entire analytic function theory, as well as of other communication technology theoretical problems. The theory of entire analytic functions is a valuable tool in communication theory and practice because entire analytic functions in the complex plane corresponding to the functions with limited spectra on the real axis. The latter are just functions that describe signals transmitted over the bandlimited communication channels. In this way, it turns out that the well-known sampling (Kotelnikov) theorem is merely the special case of Lagrange’s interpolation formula of entire analytic functions enabling also other sampling possibilities including nonuniform sampling. Similarly, other new possibilities appear in signal approximation and in approximation error evaluation, as well as in signal restoration if only partial information about the signal is known.
The following main topics are covered in this study course: entire analytic functions and their application in signal sampling, approximation, and restoration; properties of Fourier transform; signal multiplexing in multichannel systems, CDMA systems; the negentropy principle of information and its meaning for telecommunications; the influence of quantum effects on signal transmission; quantum communications; quantum cryptography; quantum computers; stochastic resonance.