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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 ____________
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