tags: mus-407 music waveform
Root mean square (RMS)
The root mean square (RMS) is the square root of the mean of a sequence of squared values:
$$x_{RMS}=\sqrt{\frac{x^2_1+x^2_2+x^2_3+...+x^2_n}{n}}$$
RMS has several applications, one of which is tracking the [amplitude] of an [audio signal].
Why RMS in audio?
What happens if we average sinusoidal values over a period of time?
- Positive and negative values will cancel, resulting in a zero average
RMS means we take the square root of the mean of a sequence of squared [sample] values:
$$x_{RMS}=\sqrt{\frac{x^2_1+x^2_2+x^2_3+...+x^2_n}{n}}$$
This always produces non-negative values, provides more meaningful measurement, and more accurately reflects continuous signal power.
- results are closer to human perception than a direct average
- provides more relevant information about the power level of a signal
RMS Tracking
General steps:
- Start with original signal
- Take the square of each value
- Over some time interval, find the average level across that interval
- Take the square root of those means (to reproduce a similar level to original signal)
