# Average Power of a Signal

Discussion in 'Miscellaneous [BG]' started by Bassline_Delux, May 1, 2006.

1. ### Bassline_Delux

Dec 24, 2003
London, England
A sinusoidal signal s(t) = A sin(&#969;t + &#952 can be expressed as a sum of two components:
s(t) = A sin&#969;t cos&#952; + A cos&#969;t sin&#952;

Show that the average power of this signal is equal to the sum of the average powers of its two components.

For the love of god. Could someone help me out on this one. My brain is imploding.

2. ### Mike MoneyIn Memoriam

Mar 18, 2003
Bakersfield California
Avatar Speakers Endorsing Hooligan
11.

3. ### J_C_L

Apr 25, 2006
Some of this is pretty foggy in what's left of my mind.

Take the integral of the square (I think) of the first representation of the signal to find the average power (it's really v^2/R, but the Rs are constant and will cancel out).

Then take the integral of the squre of each of the pieces of the signal for the second representation. Then add this together. Show this equals the integral of the first representation and you are done.

But you may really be asking how to integrate these things. On that I have no recollection, my calculus is decades gone from my mind.

Doubt that helps much, but there you go.

It also occurs to me that this might be easy to do in the frequency domain. If that is the case, then convert these to a frequency domain representations and do the power calculations on the spectrum, rather than on the time domain representation.