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Progress in the Soviet Union on the theory and applications of bandlimited functions

An approach to the study of a wide class of linear systems and bandlimited signals is discussed. The mathematical method used is the applied branch of the well-developed theory of analytic entire functions of exponential type. The unified theory provides an adequate solution for problems, which are common to information theory, antenna pattern and filter design, optics, automatic control, and others. Sampling expansions are based on the entire function interpolating theory and are applied to the time discretizing and amplitude quantization. The synthesis problems are taken from the antenna synthesis theory and use the mean-square approximation with double orthogonal functions and also Chebyshev approximation with weighted polynomials. All synthesis problems are solved with a fixed parameter by which an implementation complexity is characterized. The reconstruction problems of the input from the linear system output is mixed with noise, of deconvolution, are discussed. The received results make the system resolution limit accurate. The problem of the finite control using mean-square metric is considered.