I would like to know how physically (mathematically, maybe algorithm) to do Time Synchronous Averaging for signals: vibrations and velocity. I will be grateful for your answer in this matter? I work using LabView and had problems with this.
Time synchronous averaging works because when you add statistically independent noises they add like this: Variance(sum) = sum of variances. So... if you add various versions of your signal plus some random (uncorrelated noises) then your signal adds linearly, but the noise part adds according to the above. It is then easy to demonstrate that the signal-to-noise ration improves proportionally to the square root of the number of epochs used.
Combining noise sources: When two or more independent (uncorrelated, orthogonal) noise sources are combined, the following equation can be used to calculate the total equivalent noise: