RMS Averaging

The vibration level of the signal that a sensor returns is expressed in root mean square (RMS) acceleration. RMS averaging reduces signal fluctuations but not the noise floor.

The noise floor is not reduced because RMS averaging averages the energy, or power, of the signal. RMS averaging also causes averaged RMS quantities of single-channel measurements to have zero phase. RMS averaging for dual-channel measurements preserves important phase information. RMS-averaged measurements are computed according to the following equations.

Table 6. Equations for Calculating RMS-Averaged Measurements
Measurement Equation
FFT spectrum
X * ⋅ X
Power spectrum
〈 X * ⋅ X 〉
Cross spectrum
〈 X * 〉 ⋅ 〈 Y 〉
Frequency response
H 1 = ( X * ⋅ Y ) ( X * ⋅ X ) H 2 = ( Y * ⋅ Y ) ( Y * ⋅ X ) H 3 = ( H 1 + H 2 ) 2
Coherence
Y 2 = | < X * ⋅ Y > | 2 < X * ⋅ X > < Y * ⋅ Y >
Coherent output power
C O P = y 2 < Y * ⋅ Y >

where

X is the complex FFT of signal x (stimulus)

Y is the complex FFT of signal y (response)

X* is the complex conjugate of X

Y* is the complex conjugate of Y

(X) is the average of X, real and imaginary parts being averaged separately.