The sounds we hear are rarely one thing, in fact sounds convey meaning by changing and combine tonal and atonal elements. Nevertheless engineers will spend a lot of effort using tones (single notes) to investigate frequency response and non-linearity. Similarly we measure noise to try to understand how much there is. In our world background noise is an irremovable feature. A recording system adds noise as do distribution and replay systems. If we are to design or specify or compare, we need a framework within which to be able to estimate the significance of measurements of different sounds and signals.
Human hearing has at least six nonlinearities that should be taken into account when we evaluate the properties of music signals or reproduction systems, these are threshold, compression, selectivity, response to sound envelope, object externalisation and context (including memory).
Some of these are simpler than others to predict but let's just look at how we can decide the equivalence between tonal signals and noise.
The human hearing system features frequency selectivity which (in the steady state) can be thought of as an array of approximately 3500 filters whose bandwidth depends on the centre frequency and level; it is most selective for quiet sounds. Although the neural system is capable of extracting a huge amount of information from this filter bank, at the energy level, sounds that are close together in frequency accumulate intensity that can lead to detection or to an impression of loudness. So if we are presented with a wideband noise our hearing will broadly accumulate intensity within each band of noise or signals or both. To correctly estimate the audibility of a noise or the threshold of a tone in noise, knowing this bandwidth in context is essential.[12]
Figure 1 shows a plot of ERB, the equivalent rectangular noise bandwidth for signal at 20dB SPL. We can use this information in two ways:
To map a noise signal to its effective loudness so we can compare it with a tone. The wider the bandwidth the more a noise will accumulate intensity—see Figure 2.
To map a tonal threshold so we can compare it to a noise—see Figure 3. [12][14].
The visualisation in Figure 2 helps to estimate audibility but for a coding system we need to see the information content more clearly. We can estimate the information content in a signal by examining the area it projects onto a Shannon diagram and in these cases it is useful to not weight measurements of noise according to human psychoacoustics but rather to remap the human hearing-threshold for tones onto a uniformly exciting-noise at threshold. This noise has the shape shown in the orange curve in Figure 3 and has the very interesting property that if we gradually increase such a noise in level from below audibility, at a certain point (plotted on the graph), unlike white noise, it will become detectable at all frequencies simultaneously.
Temporal Precision There is misunderstanding of temporal accuracy in a digital channel. In our communications we refer to 'blur', but commentators tend to think we are discussing timebase. Here's a typical one:
Time resolution in digital is infinite!
A major failing of audio systems is that there is no clear end-to-end specification. We can have individual components or parts of the chain with wide bandwidth or low noise, but the final result depends on the narrowest part of the pipe. This is one reason there has been so much confusion around high-sample-rate audio—there is less point in 192kHz sampling if the amplifier stops at 20kHz.
For those interested we strongly recommend reading and absorbing the concepts covered in [1] which is only two pages long but covers a lot of ground. The most important points being made relate to temporal dispersion of signals between the performance and listener and rooting the targets in the analogue, not digital domain. The paper Stuart and Craven presented to AES in 2014 goes much deeper into the 'why' but takes more effort to grasp! [2]
Let's do another tutorial:
