5.14 - How can a 16-bit word length be enough to record all the detailin music? Doesn't that mean that the sound below -96 dB gets lost in thenoise? Since it is commonly understood that humans can perceive audiothat IS below the noise floor, aren't we losing something in digitalthat we don't lose in analog?
Description
This article is from the Audio Professional FAQ, by with numerous contributions by Gabe M. Wiener others.
5.14 - How can a 16-bit word length be enough to record all the detailin music? Doesn't that mean that the sound below -96 dB gets lost in thenoise? Since it is commonly understood that humans can perceive audiothat IS below the noise floor, aren't we losing something in digitalthat we don't lose in analog?
You're correct in saying that human hearing is capable of perceiving
audio that is well below the noise floor (we won't say what kind of
noise floor just yet). The reason it can do this is through a process
the ear and brain employ called averaging.
If we look at a single sample in a digital system or an instantaneous
shapshot in an analog system, the resulting value that we measure will
consist of some part signal and some part ambiguity. Regardless of the
real value of the signal, the presence of noise in the analog system
or quantization in the digital system sets a limit on the accuracy to
which we can unambiguously know what the original signal value was. So
on an individual sample or instantaneous snapshot, there is no way
that either ear or measurement instrument can detect signals that are
buried below either the noise or the quantization level (when properly
dithered).
However, if we look at (or listen to) much more than a single sample,
through the process of averaging, both instruments and the ear are
capable of detecting real signals below the noise floor. Let's look at
the simple case of a constant voltage that is 1/10th the value of the
noise floor. At the instantaneous or sample point, the noise value
overwhelms the signal completely. But, as we collect more consecutive
snapshots or samples, an interesting thing begins to happen. The noise
(or dither) is random and its long term average is, in fact, 0. But the
signal has a definite value, 1/10. Average the signal long enough, and the
average value due to the noise approaches 0, but the average value of
the signal remains constant at 1/10.
A somewhat analogous process happens with high frequency tones. In
this case the averaging effect is that of a narrow-band filter. The
spectrum of the noise (or simple dither) is broadband, but the
spectrum of the tone is very narrow band. Place a filter centered on
the tone and while we make the filter narrower and narrower, the
contribution of the noise gets less and less, but the contribution of
the signal remains the same.
Both the ear and measurement instruments are capable of averaging
and filtering, and together are capable of pulling real signals from
deep down within the noise, as long as the signals have one of two
properties: either a period that is long compared to the inherent
sampling period of the signal in a digital system or long compared to
the reciprocal of the bandwidth in an analog system, or a periodic
signal that remains periodic for a comparably long time.
Special measurement instrument were developed decades ago that were
capable of easily detecting real signals that were 60 dB below the
broadband noise floor. And these devices are equally capable of
detecting signals under similar conditions in properly dithered
digital systems as well.
How much the ear is capable of detecting is dependent upon many
conditions, such as the frequency and relative strength of the tone,
as well as individual factors such as aging, hearing damage and the
like.
But the same rules apply to both analog systems with noise and digital
systems with decorrelated quantization noise. [Dick]
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