Order Cuts And Overall Level

Order cuts are taken from a set of FFTs, each one at a different rpm. The rms level is then found as the Square root of the Sum of the squares of each of the FFT values. Mathematically, if x_{ks} is the modulus (magnitude) of the k^{th} value of the FFT at speed s for k = 1,\dots,N-1 then the rms value at that speed is given by

rms_s = \sqrt{\sum_{k=0}^{N-1}{x_{ks} ^2}}

This takes into account the entire energy at that speed both the order and the non order components, including any noise.

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Dynamic Range And Overall Level : What Are They ?

Accurate measurement of a signal depends on the dynamic range and the overall level of the data acquisition system. The overall level setting may be thought of as determining the largest signal that can be measured. This clearly depends on the present gain setting. That is the overall level is related to the gain. Clearly if the overall level is too small (gain too high) then the signal will be clipped and we will have poor quality data. The dynamic range then tells us that for the given overall level what is the smallest signal we can measure accurately whilst simultaneously measuring the large signal.

In a very simple sense suppose we have an artificial signal which consists of a sinewave at a large amplitude A for the first half and that this is followed by a sinewave with a small amplitude a for the second half. We will set the gain (the overall level) to allow the best measurement of the A sinewave. The dynamic range tells us how small a may be so we can also measure that without changing settings.
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Time Varying Overall Level Vibration (or Noise)

A common requirement to measure overall level vibration (or noise) as a function of time. Now, the overall level is a measure of the total dynamic energy in the signal. That is it does not contain the energy due to the DC level, which is the same as the mean value. The overall level is often loosely referred to as the signal RMS value. However the formal definition of the RMS level is that it contains the DC level as well as the dynamic energy level. If only the dynamic contribution is required then the measure needed is, strictly speaking, the Standard Deviation (SD). Sometimes it is useful to refer to the SD as the Dynamic RMS.

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