Among the following functions, which one has period $\frac { \pi } { 2 }$ and is monotonically increasing on the interval $\left( \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)$?
A．$f ( x ) = | \cos 2 x |$
B．$f ( x ) = | \sin 2 x |$
C．$f ( x ) = \cos | x |$
D．$f ( x ) = \sin | x |$