Assuming one wants a frequency spectrum from an acquired time measurement, it is generally accepted that averaging of a signal in the time domain is not very useful due to the randomness of the start of the time block used to calculate the Fourier transforms to be averaged. If there is a way to synchronize the start of the time block to a periodic event in the signal, then averaging in the time domain is possible and can be very useful.
To demonstrate the usefulness of averaging time signals, a random time signal and a pulse time signal are generated and summed.
When the time signal of the pulse is embedded into the time signal of the random signal, the pulse signal becomes totally indistinguishable in the time domain and only barely distinguishable in the frequency domain figure.
As seen in the figures above, finding the spectrum of the pulse signal does not yield much usable information even when averaging of the spectrum is performed. The question is, how can the “noise” (random signal) be minimized so that the spectrum of the pulse can be seen?
Time domain signal averaging is only applicable if the signal is stationary (in the statistical sense). If the start points of the analysis time blocks are synchronized to the pulse, these time blocks will be random with respect to the random signal. Consequently the components of the signal uncorrelated to the pulse data will average towards zero.
Once all the time averaging is completed, the pulse signal or any signal correlated to the pulse signal should remain and any uncorrelated signals should average towards zero. The results of the time averaging of the above signals are shown in figures 7 & 8.
It is reasonable to ask how this be used in real world. Time domain synchronous averaging is most applicable to situations when measurements are being made on constant speed rotating machinery in very noisy environments. To evaluate the vibration from a motor or gearbox which are engulfed in an environment of high levels of uncorrelated noise. This might be a motor/gearbox driving a tumbler used for mixing or polishing. An automotive applications could include the desire to extract the powertrain noise or vibration signals while driving over a very rough surface. Any application where the desired signals are correlated to a trigger signal from the test specimen has a potential for making this a viable method of extracting the desired signals.