Variance of white noise

Started by Tom Killwhang September 28, 2020
I was reading Box and Jenkins Time series analysis and noticed that when they calculated power spectrum they had a factor 2 in the numerator - see

equation (3.1.12).

I couldn't figure out where the 2 is coming from but then I wondered if they define noise a different way in stats. Just like when we have sine waves and take an FFT the magnitude is divided by 2 when we show the two sided spectrum, is it fair to do the same with white-noise? I think them may have multiplied it by 2 so that for the full spectrum =pi to +pi it gets halved. We don't seem to do this in engineering do we?