An analysis used for the overall amplitude of a signal is called the root-mean-square (RMS) amplitude or level. Conceptually, it describes the average signal amplitude. However, it is different than simply measuring the arithmetic mean of a signal.

 

An audio signal can have both positive and negative amplitude values. If we took the arithmetic mean of a sine wave, the negative values would offset the positive values and the result would be zero. This approach is not informative about the average signal level.

 

This is where the RMS level can be useful. It is based on the magnitude of a signal as a measure of signal strength, regardless of whether the amplitude is positive or negative. The magnitude is calculated by squaring each sample value (so they are all positive), then the signal average is calculated, eventually followed by the square root operation. More completely, the RMS level is, “the square root of the arithmetic mean of the signal squared.”

 

RMS Definition
 

 

We can use the RMS level as a reference while changing the amplitude of a signal. This is called RMS Normalization.

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