Continuous Time Fourier in LTI system

[beanus]

Homework Statement

Homework Equations

Not sure

The Attempt at a Solution

No idea how to even begin.

I don't even know how to start this equation. My textbook has no examples of this type. Do I need to transform x(t)? If someone could simply steer me in the right direction I'm confident I can figure it out.

 

[aralbrec]

I don't even know how to start this equation. My textbook has no examples of this type. Do I need to transform x(t)? If someone could simply steer me in the right direction I'm confident I can figure it out.

For Part A. You can solve this several different ways. If you don't know what to do, you should always resort to the definition of power. But in this case you should know that you can also find the power of a signal from its Fourier transform and this particular signal has a really simple Fourier transform. Normally I would just compute the power of the sinusoids from rms values but part A is leading into part B.

For Part B, the transfer function shows how sinusoids are transformed by the system. Your input is the sum of two sinusoids. Again, there is more than one way to do this one but the question is practically begging you to use |H| somehow. From part A you should have the spectrum of X and therefore its magnitude too.