Averaging

In any process it is often necessary to average a number of measurements to gain any confidence in the measured value. As the number of measurements increases confidence will also increase. However, care must be taken to ensure that the quantity being measured remains stationary over the averaging time.

In performing spectrum analysis, regardless of how it is done, some form of time averaging must be done to accurately determine the level of the signal at each frequency. In vibration analysis, the most important type of averaging employed is linear spectrum averaging, where a series of individual spectra are added together and the sum is divided by the number of spectra.

For broadband random signals the standard deviation can be estimated by:

where
σ = standard deviation [dB]
B = bandwidth of the signal [Hz]
T = measurement time [s]

This shows that the the wider the bandwidth the quicker the average settles.

Linear averaging smoothes out the spectrum of the random noise in a spectrum making the discrete frequency components easier to see, but it does not actually reduce the noise level.

Another type of averaging that is important in machinery monitoring is time domain averaging, or time synchronous averaging, and it requires a tachometer connected to the trigger input of the analyzer to synchronize each "snapshot" of the signal to the running speed of the machine. Time domain averaging is very useful in reducing the random noise components in a spectrum, or in reducing the effect of other interfering signals such as components from another nearby machine.

See also: Peak Hold, Smoothing.

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Subjects: Mathematics Physics