One approach to solve problems of super-noise-immune detection of signals

Some restrictions for fundamental solutions of signal optimal detection problems are considered, which arise due to the exclusive usage of functional Hilbert space metrics. To diversify criteria for deviation of an input process from the transmitted signal estimation at the expense of a number of metrics, used in different functional spaces is suggested to overcome them. Preference is given to those, which provide the greatest increase of the norm due to the signal presence. It is shown that from the point of view of technical implementation a choice of metrics and of a corresponding functional space determines the way of detection, whereas the receiver structure, i.e. the way of signal processing, is determined by the kind of a functional used in the selected functional space. An extreme value of this functional is a criterion for optimal detection in a given functional space. Basing on periodicity of the same kind or form of oscillations it is suggested to solve the main problem in a functional space formation - determination of a fixed period, meeting the conditions for the actual infinity and permitting to measure any statistical moments, including the odd ones. The most informational and economical among them, according to A. Kolmogorov, are the moments of the 1-st order. It is suggested to use them for the super-noise-immune detection of signals.