Hi,

I'm taking a signals and systems class this semester and one of the problems that I am currently working on is:

x(t) = sin(2t) - sin(2t-.1)

I know that you can compute the power of this waveform by multiplying the integral of the square of x(t) by 1/T. However, I also know that wave forms of differing frequency usually just add by using the A^2/2 method. Is there a similar formula for this instance? I don't feel like computing the integral for the square of x(t) is actually what we are supposed to glean from this coursework.

Is there a general case where the sine waves have only a phase difference (as above) and the same frequency?

Thank you for any assistance,

Brad

 

Is there a general case where the sine waves have only a phase difference (as above) and the same frequency?

Well you should at least be able to add the two terms by phasor addition to find the resulting AC function.

 

Hi,

I'm taking a signals and systems class this semester and one of the problems that I am currently working on is:

x(t) = sin(2t) - sin(2t-.1)

I know that you can compute the power of this waveform by multiplying the integral of the square of x(t) by 1/T. However, I also know that wave forms of differing frequency usually just add by using the A^2/2 method. Is there a similar formula for this instance? I don't feel like computing the integral for the square of x(t) is actually what we are supposed to glean from this coursework.

Is there a general case where the sine waves have only a phase difference (as above) and the same frequency?

Thank you for any assistance,

Brad

First, are you looking for the power or the average power?

What do your trig identities tell you about

sin(ωt) - sin(ωt-θ)

Or, what happens if you square this and examine it before you take the integral? Can't the integral of two of the terms be done by inspection? Then you can apply a trig identity to the cross-term to simplify it.