Data rate limitations for observability of nonlinear systems**A. Pogromsky acknowledges his partial support during his stay with the ITMO university by Government of Russian Federation grant (074-U01), and the Ministry of Education and Science of Russian Federation (project 14.Z50.31.0031), (Sees. 1, 2, 5, 7). A. Matveev acknowledges his support by RSF 14-21-00041 and the Saint Petersburg State University (Sees. 3, 4, 6, 8).