# Average power of sinusoidal signal

1. Sep 4, 2009

### ngibson

1. The problem statement, all variables and given/known data
Question: Consider the sinusoidal signal:
A*cos($$\omega$$t + $$\phi$$)

Determine the average power

2. Relevant equations
This is my first real attempt in signals and I am really confused with the question...
I guess my question would be am I suppose to take the P = lim as t-> $$\infty$$ $$\frac{1}{t}$$ $$\int$$ A*cos($$\omega$$t + $$\phi$$) ?

3. The attempt at a solution
I have no attempted solution yet. I am really just trying to see how to start this problem and then go from there!!

2. Sep 4, 2009

### Fightfish

The average value of a function is \frac{1}{t}\int f(t) \Delta t. For sinusoidal functions, we typically average over a period.
Also, power is proportional to amplitude squared.

3. Sep 5, 2009

### Redbelly98

Staff Emeritus

Is "the signal" a voltage or a current? How much resistance is the signal connected to?

4. Sep 16, 2009

### Mr.Green

The average power of the signal x(t) is given by:

P = lim T ---> infinity * (1/T) * [ integration of x2(t) over (0 to T) with respect to t]

please ditinguish between "T" and "t". "T" is the period of the signal and "t" is the time.

If you integrate [A cos (ωt + ф)]2 over (0 to T) and take the limit as T approaches infinity you will have the answer. The result should be [A2/2]

Hint: T in the denominator will be simplified with the T in the numerator after the integration and you have no need to substitue any value instead of T.