The Definition of Arrival Signal S-Matrix-s Rank and Synthesis of Discrete Filter

S-matrix of arrival signal with dimension is considered in the paper. It-s transformed to upper overdiagonal form for finding of rank with help elementary conversions. Conditions for defining of S-matrix-s rank, which contain energy spectrum arrival signal decomposition index into two-dimensional Fourier series by cosines (ESASDI) , are obtained. Auxiliary function is introduced. Algorithm for finding the conditions allowing to define S-matrix-s rank is applied successively. Counts of impulse characteristic (IC) are calculated in accordance with S-matrix-s rank. The auxiliary function is used also. Efficiency functional wrote based known ESASDI and counts IC. Formula allowing to find the functional of efficiency depending on arrival signal S-matrix-s rank is obtained.