The Meaning of Dynamic Range and Signal-to-Noise Ratios

One of the great promises of digital audio has to do with its overall dynamic range, which can roughly be defined as 6 dB per bit, so that a 16-bit system yields 96 dB dynamic range and 20 bits yield 120 dB dynamic range. Signal-to-noise ratios fit within this range. Typically, a signal is 10-15 dB softer than the loudest possible signal (the range between the typical signal and the loudest possible signal is usually called "headroom"), and the noise floor is the sum of the powers of all of the noise floors that have become part of the signal. In a purely digital test of a digital system, that floor would be the noise floor of the digital system. "Signal-to-noise" plus "headroom" equal "dynamic range." In a 16-bit system with 15 dB of headroom, the signal-to-noise ratio would be 81 dB (96 - 15 = 81).

Such an expression is, however, theoretical. In fact, noise should be measured as the "noise of the system under test." It may be, for instance, that the noise of the A-D and D-A converters, plus analog buffer amps, plus hum from the power supply, etc., might cause the noise floor of the system to degrade from the 96 dB dynamic range that is the mathematical fruit of having 16 bits of data represent each sample, to only 86 dB dynamic range. In such a case, the dynamic range and the signal-to-noise ratio both decrease by 10 dB, to 86 and 71 dB respectively.

The point is that the noise floor is the sum of the powers of all of the noise floors the signal encounters as it passes through the system. Meanwhile, the peak level of the system is limited to the lowest peak level condition the signal encounters as it passes through the system.

This is why levels management is so very important. Noise creeps up on you, while peak capacity remains limited. At the same time, our ears have immense dynamic range (120 dB, easy), so all the audio noise warts are audible.

Meanwhile, we have to define what we mean by "system." Until I finish perfecting the neural insertion patch points I'm working on, the "system" used for recording and playback of music through loudspeakers for listeners must include the acoustical transmission paths of the recording and playback spaces. For specific hardware or software, "system" usually includes all elements of the signal path which the hardware or software affects.

So when we are engaged in music production using this equipment, and the manufacturer has, by the way he or she has configured the equipment, forced us to keep it in our faces while working, then the acoustical noise of the equipment must be included in the consideration of its overall noise performance. Which is to say, the manufacturer has injected the acoustical noise of the device into the system signal flow.

To restate an obvious fact that the various Silicon Sammies and Suzies should post in all cafeterias, lounges and restrooms: Just Because It Doesn't Exist In The Digital Realm Doesn't Mean It Isn't Real!