Handbook for Sound Engineers

Consoles 955

untoward jump in output level occurs. (As an example,
the transition from 01111111 to 10000000 in an 8 bit
word is a likely point of nonmonotonicity. Although this
only reflects one increment of resolution change, a lot
of convertor bits are changing simultaneously; the more
that have to change—especially the wider the
word—the more chance for error. Trust is being laid in
the converter’s manufacturer that each successive bit
carries exactly twice the weight of the previous one;
with very wide converters the increments of resolution
are tiny and the odds are increasingly slim. In a 16 bit
converter the most significant bit has to be accurate to
within at least a bit of resolution for the device to be
monotonic; this corresponds to an accuracy of better
than 0.0015%. Enough said. The more bits change in a
transition, each of the individual bit’s tolerances come
into play and errors are far more likely.
The almost wholesale shift to sigma-delta–type A/D
converters, which are inherently monotonic, has all but
buried this problem now in most practical circumstances.
Integrated IC sigma-delta converters are available very
inexpensively with what used to be considered
science-fiction performance. As mentioned, the primary
limitation is noise, either induced digital mush or from
the necessary analog parts in the mixed-signal format of
these devices; such is not an ideal environment for
low-level analog. The low supply rail voltages (5 V is
considered big these days) mean that the additional
dynamic range available from conventional high rails
(such as typically ±15 V or more) is simply not available.
Although it is actually quite difficult now to find a
convertor that is rated at any less than 24 bits (and to be
fair, their internal structure, in particular the word width
of the FIRs, is 24 bit), the actual performance depends
on how many of those bits represent useful data and
how many are marketing bits.

25.18.1.2 Sampling Rate

In addition to the required resolution, speed of conver-
sion plays a great part. In order to give an accurate
portrayal over time of an input signals waveshape, there

need to be enough conversions for the digitized signal to

be reconstructed to an exact analog of the original

signal. The lowest theoretical (Nyquist) sampling rate is

twice the highest frequency intended to be processed.

This implies at least two digital word conversions taking

place for each cycle of (typically in audio) 20 kHz. In

practice the sampling rate is made even higher, and

figures of 44.1 kHz (domestic) and 48 kHz in profes-

sional audio are the most common, 96 kHz and higher

yet looming and in search of a mainstream application.

25.18.1.3 Convertor Limitations and Requirements

Currently the figures of 24 bit linear conversion at a

48 kHz rate are de facto standard values in pro audio.

Although these parameters are capable of very respect-

able sonic performance, certainly comparable or in

excess of the analog recording and transmission

methods digital has supplanted, their practical imple-

mentations fall somewhat short of the performance of

analog electronics. This is not a snipe at digital; it is

clear to anyone who chooses to investigate that the

practical differences are small.

The first question is of how much resolution is actu-

ally required. A good quiet balanced-bus multitrack

console’s typical input-output path can be expected to

have some 26 dB head room above an operating level of

0 dBu and a noise floor some 90 dB below that for a

116 dB dynamic range. A similar quality mixer

summing a fair number of sources can still be reason-

ably expected to have a noise floor of 80 dBu corre-

sponding to 106 dB dynamic range. These values imply

digital word widths of some 20 bits and 18 bits, respec-

tively. converters of these capabilities are readily avail-

able commercially, if implemented well. A further

related question is what is the highest dynamic range

signal source? A very good condenser microphone with

a very quiet FET in it in a very quiet room is probably

the best candidate; it might be able to cope with a

130 dB SPL gunshot at the high end of the range while

still hearing breathing noises in the room at the other.

Why one might want, other than as a science experi-

Figure 25-126. A basic digital signal processor in an analog world.

Input gain

amplifier

Anti-aliasing

filter

Sample

and holdAnalog/digitalconverter

Program

memory

DSP

Data

memory

Digital/analog

convertor

Reconstruction

filter

Analog input Analog output