One type of predator can find both male and female katydids, bats. In areas where katydid hunting bats and katydids overlap, the males have a song that is very brief at the frequency that can be heard by the bats. The males add a trill to their song in a frequency that bats do not hear. This makes the males more difficult for the bats to locate while the females can focus on the high frequency trill. Bats have been found to prey on both males and females of these katydid species, when they can find them.
JACQUELINE J. BELWOOD & GLENN K. MORRIS. 1987. Bat Predation and Its Influence on Calling Behavior in Neotropical Katydids. Science 2 October 1987. Vol 238: 64-67.