The Whittacker-Kotelnikov-Shannon Interpolating Theory Applications

The sampling theorem gives ideal mathematic model for technologic potential possibilities. The generalizing by spectra superimposing gave opportunity for connecting any multidimension spatial grids with optimal spectral finite sets, which cowered without crossing the all spectral space. The reproduction it is possible with using the filters Nykwist frequency limited outputs. For practical example circular finite space the reproduction used the radial samples. Besides the superimposing used another sampling methods. If the samples functions and its derivations it is possible of bringing together samples, the deduction for samples functions zeros and using the general interpolation solution. The rate transmitting Shannon communication channel calculation using the sampling theorem must be indicated. The useful properties of sampling series with given numbers were exposited be the weighted polynomials. For example, the problem of maximizing antennas gain was solved. If the probability density measured on quantized data, the sampling representation was used for cut off spectra interpolations was synthesized. The sampling theorem gives opportunity to calculate the control signals for linear system turning of, for example, in pipes or cyclic accelerators. The universal dependence AD-DA error from quantizing steps and discrete intervals for classical probability densities occurred by gaussian functions was calculated. The problem calculating the object dimensions by diffraction exposure was interested for technology and science. The optimum decision is impossible, if the object intensity was approximated by the constant, so it was necessary to introduce the next Fourier coefficient. The problem the board instrument calibration it was imported for distance sounding the Earth from space by using the aircraft copies data. For employing it is useful to approximate the results by sampling series. The distance space data from instruments with known directivity characteristics represented by cardinal series were used for employing the sets of virtual directivity solutions useful for applied problems, for example, the eliminate the sidelobes of directivity.