Consider an LTI system with magnitude response
$\left | H(f) \right |=\left\{\begin{matrix} 1-\frac{\left | f \right |}{20} &, \left | f \right |\leq 20 \\ 0&, \left | f \right |> 20 \end{matrix}\right.$
and phase response
$\arg \left \{ H(f) \right \}=-2f.$
If the input to the system is
$x(t)=8 \cos (20\pi t+\frac{\pi }{4})+16\sin (40\pi t+\frac{\pi }{8})+24\cos (80\pi t+\frac{\pi }{16}),$
then the average power of the output signal $y(t)$ is ____________
