When did signal processing become a field of its own?
There's a nice historical account given by the IEEE Signal Processing Society, that references 1948 as the year the field began. I'm not sure if that's necessarily accepted as "official" by other sources, but their reasoning is pretty convincing (at least as a ballpark):


  The year 1948 may be regarded as the annus mirabilis in the emergence
  of the discipline of signal processing. For in that year Claude
  Shannon published the epoch-making "A mathematical theory of
  communication"; Bernard Oliver, John Pierce, and Claude Shannon
  published the classic argument for the use of pulse-code modulation;
  modern digital methods of spectrum estimation were introduced;
  error-correcting codes were introduced; audio engineering achieved a
  new prominence; and the IEEE Signal Processing Society, albeit under a
  different name, was established.


That quote is from the beginning of the second chapter, Annus Mirabilis: 1948.