Sidebar: A VU of RMS

The amplitude of a audio waveform is directly related to it’s “pressure” height above zero pressure and/or voltage. Unfortunately, the amplitude of the voltage that is creating the waveform is always changing. If we simply take an average of that swinging voltage, our result is approximately zero, which doesn’t do at all. So we normally use another measurement technique called RMS (Root Mean Square – don’t worry about the math) that derives a signal level from the changing voltage that expresses its power relative to a DC (direct current - not an audio signal) voltage. For a sine wave, that RMS value is about .7 of the peak positive voltage of the sine. For a square wave it is the same as the peak voltage. So, the RMS level depends on the shape of the wave, what the calculistas call the “area under the curve.” See Figure 2.

	Figure 2. A sine wave with 1 volt peak amplitude (2 volts peak-to-peak) and a .7 volt RMS level.

It gets more complicated, due to the nature of time. Usually, RMS levels of changing signals are expressed on a meter as an integrated average RMS level over the preceding second or so of time, so what the meter is telling you is not what the level is now, but what its average over the most recent second was. Such a meter is easy to read (the needle moves nice and slowly, kind of like it was embedded in molasses on a chilly November morning), but it lacks a certain, er, musical relevance.

	Figure 3. A sine wave with changing amplitude. The RMS voltage level will change over time as shown by the heavy line. This line represents the output of the envelope follower in a compressor. With various modifications (polarity reversal, attenuation and amplification, delay, rectification and offset), it is this signal that controls the VCA in the compressor.

As a result, many years ago, somebody devised a meter that indicated level as equivalent to how humans hear speech, so that the meter’s action expressed visually an equivalence to the subjective loudness level of talking heads (actually this was before TV – they didn’t have the heads yet, just the talking). They called this measuring system Volume Units, and such meters were called Volume Unit Meters, or VU meters. The name stuck but the Volume Unit itself has been pretty much abandoned. Most so-called VU meters today have a sort of speeded-up RMS action. And, because everybody is obsessed with overload today (“Oh, no! Not more overload, today of all days! I can’t stand it! I swear this time I’m going into distortion!”), we’ve started to use so-called “peak” meters a lot. These meters express the highest level during the last second or so. They aren’t, er, musically relevant either, but they are handy for detecting how close your audio signal is to the threshold of distortion.

One final thing: the concept of crest factor. Crest factor is the ratio (in dB) between the long-term RMS value of a signal and its peak RMS level. A steady-state sine wave has a crest factor of 0 dB, because its peak level and its average level are the same. Pink noise, on the other hand, has a crest actor of about 12 dB, which is to say that there will be peaks up to 12 dB louder than average in the statistically random signal called noise. Music is sort of similar to noise in this regard, until you include dynamics and silent time. Vocals have a comparatively low crest factor, most of the time, while percussion has a large crest factor. It is useful, from both production and engineering standpoints, to listen to music in terms of its crest factor. Changing the crest factor will change the mood and quality of the music significantly.

Why am I talking about this in an article about compressors? Because it is important to keep in mind that there is no single definition of amplitude, let alone loudness, and compressors allow you, through the attack and release time controls, to have access to the averaging and integrating circuits that allow you to define amplitude over time in a way that is musically relevant to you for each specific instance.