William F. Egan

William F. Egan (1936 – December 16, 2012[1]) was well-known expert and author in the area of PLLs.

In 1981, describing the high-order PLL, William Egan conjectured that type II APLL has theoretically infinite the hold-in and pull-in ranges.

[2]: 176 [3]: 245 [4]: 192 [5]: 161  From a mathematical point of view, that means that the loss of global stability in type II APLL is caused by the birth of self-excited oscillations and not hidden oscillations (i.e., the boundary of global stability and the pull-in range in the space of parameters is trivial).

A similar statement for the second-order APLL with lead-lag filter arises in Kapranov's conjecture on the pull-in range and Viterbi's problem on the APLL ranges coincidence.

[11][12] In general, his conjecture is not valid and the global stability and the pull-in range for the type I APLL with lead-lag filters may be limited by the birth of hidden oscillations (hidden boundary of the global stability and the pull-in range).