Windowing In Vibration Analysis

What is windowing?

In vibration analysis, Windowing is a technique that is used on Fast Fourier transforms, which allows us to see the data (frequency vs amplitude) in a specific way, which in turn depends on the obtaining and analyzing an FFT vibration spectrum.

FFT spectrums (which is actually a presentation of Frequency Domain Data) are obtained from a time series data, which we call as a Time Domain Analysis. The idea of having a time domain analysis is to see how a signal repeats itself. In order to do that we select a time range that would capture such a repetition. It is said that with a time series data we “go” to the phenomenon (in our case vibration) to understand it. Similarly, it is said that with an FFT signal we allow the phenomenon to “come” to us like the waves of the sea rushing to meet us on the shore. We see the same phenomenon in two different ways. But the phenomenon is essentially repetitive or periodic in nature.

But what happens if a signal is not exactly periodic within the time record? When we collect a vibration spectrum through a data collection system, the amplitude of vibration is divided into multiple, adjacent frequency bins. This is true but it’s actually a bit worse than that. If the time record does not start and stop with the same data value, the signal can actually smear across the entire spectrum. This smearing will also vary wildly between records because the amount of mismatch between the starting value and ending value changes with each record.

Therefore, Windows are mathematical functions defined across the time record which are periodic in the time record. They start and stop at zero and are smooth functions in between. So, when the time record is windowed, its points are multiplied by the window function, time-bin by time-bin, and the resulting time record is by definition periodic. It may not be identical from record to record, but it will be periodic (zero at each end).

Such a method to convert a non-periodic signal into a periodic signal is known in vibration analysis as “forced periodicity.”

But the question is how would an analyst guess the presence of such non-periodic signal hidden within FFT spectrums? One good way would be to look at a waterfall plot of the FFT spectrums — i.e. spectrums arranged one after the other as per their time and date of capture. If we are able to spot an odd frequency as a stand alone peak somewhere in the spectrum, which fails to appear in other spectrums, we may possibly guess that to be a non-periodic signal .

Important to understand that windowing is applied to both time domain and frequency domain representations.

© Dibyendu De