DSP Robotics Support

Hi,

Working on an RMS compressor.
To test if the envelope follower is correct, I injected a 1 KHz sine wave tone at (-12 dBFS).
The envelope follower reads (-15 dBFS) which (I guess) is expected due to 'crest fector' of sine waves which is (-3 db).
That means that the 'distance' between a peak and RMS of a sine wave is (-3 dB).

So, is all of this correct? Should I expect an RMS compressor to 'read' a sine wave signal at 3 db lower than its rating?
Had I used professional measuring gear (generator and analyzer) - and dialed in a sine wave signal, will the 'knee' of the RMS compressor run at (-3 db) lower than intended?

yes, that is correct. RMS is short for root mean square, which means you square each value, sum them all up, divide by number of values and take square root or in other words is is the square root of arithmetic mean of squares. Square of a sin(x) is 0.5+0.5*sin(x). Since sin(x) is symmetric, the average value is 0.5. Square root of that is about 0.702 which is equivalent to -3.01dB.
In fact, this -3dB difference between peak and RMS is generally true on average. The phases of the individual harmonics must be specially aligned to deviate from this average - the edge cases being square wave, where the phases are aligned in such a way that peak and RMS equal and impulse where the phases are so aligned that they cancel out everywhere except one point.

In addition to KG:

For sine waves (and only for them) there's a law. It says that the RMS of a sine is always

(1 / squareroot of 2) * amplitude

So, there's 0.707 again for an amplitude of 1 (I think KG meant 0.707).