RMS and Leq

The vibration level of the signal that a sensor returns is expressed in root mean square acceleration (grms). Leq is the RMS sound level with the measurement duration used as the averaging time. Calculating these provides a concise representation of fluctuating noise levels.

The RMS level of a continuous acceleration signal from time t1 to time t2 is given by the following equation:

g rms = 1 t 2 − t 1 ⋅ ∫ t 1 t 2 g 2 ( t ) d t

where t2 – t1 is the integration time or measurement time.

The RMS level of a discrete acceleration signal is given by the following equation.

g rms = 1 N ⋅ ∑ i = 1 n g i 2

The linear averaging, or equivalent continuous sound level (Leq), is one of the time-averaging modes in sound level measurements. You compute the Leq by integrating the square of the signal over a fixed-time interval and dividing by the time interval.

The Leq of a continuous signal from time t1 to time t2 is given by the following equation:

L e q = 10 l o g ⁡ 10 1 ( t 2 − t 1 ) ∫ t 1 t 2 ( p ( t ) p o ) 2 d t

where

P 0 is the reference pressure of 20 μPa for acoustics.

The Leq of a discrete signal is given by the following equation:

L e q = 10 log ⁡ 10 ( 1 N ⋅ Σ i = 1 N ( p i 2 p 0 2 ) 2 )