Removing A-Weighting From Time History Signals

It sometimes occurs that signals are captured with A-weighting applied to the data by the acquisition device. This can be a problem if, for example, you wish to use the data in a hearing test or to use it for a structural vibration analysis. Now, A-weighting allegedly mimics what the ear does to a signal. If we play back an A weighted sound then we perceive a double A-weighted signal which is clearly not intended. When doing structural work it is usually the lower frequencies, say 2kHz or less, that is generally required. A-weighting seriously attenuates the low frequencies and also applies gain above 1kHz.

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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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