Power contained in a periodic signal (complex exponentials)

[Jd303]

Compute the power contained in the periodic signal x(t) = 10.0[cos(160.7πt)]^4

The problem I have is I end up with a constant value for ak for all values of k
-I start by using inverse Euler formula
-Do the appropriate integration
-Then consider k for odd and even values

My working is attached, if anyone is able to show me the correct procedure, or is able to shed some light for me to understand the topic better it would be much appreciated.

 

[rude man]

Power = energy per integer number of periods/time of that number of periods
= ∫x(t)²dt over n periods T/nT.

An expansion I found that might be useful is
cos⁴(x) = (1/8)[3 + 4cos(2x) + cos(4x)].

 

[Jd303]

Thanks for the expression, I have since found that i had a calculation error, but fixing this up leaves me with a result of 0. I have tried this both using exponentials and trigonometric identities both yielding a final answer of 0.

Can anyone point me in the right direction or plot out some steps?

 

[rude man]

Thanks for the expression, I have since found that i had a calculation error, but fixing this up leaves me with a result of 0. I have tried this both using exponentials and trigonometric identities both yielding a final answer of 0.

Can anyone point me in the right direction or plot out some steps?

Perform the integration!