Weighted Hilbert transformation

Generalization of transformation of Hilbert, determined as the self-weighted transformation of Hilbert and which arises up at description physical distribution of signal and reflection of him from borders, is considered in the real article. Properties of this transformation are studied. The concept of analytical signal is adapted to the self-weighted transformation of Hilbert. As classic transformation of Hilbert appears as the special case of this transformation. Intercommunication of coefficients of the generalized transformation of Hilbert is found with properties of environment.