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4 Introduction
a periodic clock signal fed to the ADC and DAC, although there is no reason why
both need the same sample rate – digital processing can be used to change sample rate.
Using the well-known Nyquist criterion, the highest frequency that can be
unambiguously represented by such a stream of samples is half of the sampling rate.
Samples themselves as delivered by ADC are generally fixed point with a resolution
of 16 bits, although 20 bits and even up to 24 bits are found in high-end audio systems.
Handling these on computer could utilise either fixed or floating point representation
(fixed point meaning each sample is a scaled integer, while floating point allows frac-
tional representation), with a general rule of thumb for reasonable quality being that 20
bits fixed point resolution is desirable for performing processing operations in a system
with 16-bit input and output.
In the absence of other factors, the general rule is that an n bit uniformly sampled
digital audio signal will have a dynamic range (the ratio of the biggest amplitude that
can be represented in the system to the smallest one) of, at best:
DR(dB) = 6.02 × n. (1.1)
For telephone-quality speech, resolutions as low as 8–12 bits are possible depending on
the application. For GSM-type mobile phones, 14 bits is common. Telephone-quality,
often referred to as toll-quality, is perfectly reasonable for vocal communications, but is
not perceived as being of particularly high quality. For this reason, more modern vocal
communication systems have tended to move beyond 8 bits sample resolution in practice.
Sample rates vary widely from 7.2 kHz or 8 kHz for telephone-quality audio to
44.1 kHz for CD-quality audio. Long-play style digital audio systems occasionally opt
for 32 kHz, and high-quality systems use 48 kHz. A recent trend is to double this to
96 kHz. It is debatable whether a sampling rate of 96 kHz is at all useful to the human
ear which can typically not resolve signals beyond about 18 kHz, apart from the rare
listeners having golden ears.
1
However such systems may be more pet-friendly: dogs
are reportedly able to hear up to 44 kHz and cats up to almost 80 kHz.
1
The die-hard audio enthusiasts who prefer valve amplifiers, pay several years’ salary for a pair of
loudspeakers, and often claim they can hear above 20 kHz, are usually known as having golden ears.
Infobox 1.1 Audio fidelity
Something to note is the inexactness of the entire conversion process: what you hear is a wave
impinging on the eardrum, but what you obtain on the computer has travelled some way through
air, possibly bounced past several obstructions, hit a microphone, vibrated a membrane, been
converted to an electrical signal, amplified, and then sampled. Amplifiers add noise, distortion,
and are not entirely linear. Microphones are usually far worse on all counts. Analogue-to-digital
converters also suffer linearity errors, add noise, distortion, and introduce quantisation error due
to the precision of their voltage sampling process. The result of all this is a computerised sequence
of samples that may not be as closely related to the real-world sound as you might expect. Do not
be surprised when high-precision analysis or measurements are unrepeatable due to noise, or if
delicate changes made to a sampled audio signal are undetectable to the naked ear upon replay.