In this case the 4
th
overtone of a fundamental tone
of 4.5 kHz will generate aliasing distortion at 21.6 kHz.
This frequency will modulate with the other tones in
the signal spectrum, and first order modulation with
the 3
rd
overtone will then generate a modulation
frequency of 3.6 kHz, which is likely to be audible and
make interference with the original signal. IM
distortion coming from modulation between the
harmonics of the signal will not generate a-harmonic
distortion signals, since the IM products will have
frequencies equal to the harmonic of the signal, and
will therefore not be audible.
DVD audio
Recently the new sampling 96 kHz format has been
defined. This format is meant to be used in the music
production environments, and as the DVD linear audio
format. Generally, there is an acceptance that this
higher sample-rate gives a better sound quality due to
the extended signal bandwidth from 48 kHz to 96 kHz.
However, sampling with 96 kHz having 0.45/0.55
filters – which is currently the case for most converters
– the aliasing distortion will move up in a frequency
area where the IM distortion has very little effect since
the harmonic contents of audio signals are insignificant
above 40 kHz. An interesting test is to compare the 96
kHz sampled signals with the 44,1 kHz sampled signals
having NF stop-band filtering. At 96 kHz sampling
the ultra-sonic harmonics will be present in the signal
giving a better quality than when sampled with 44.1/
48 kHz even with a NF stop-band filter applied.
However the primary issue when considering the
different sample-rates for high quality sampling is to
avoid AID, more than having a higher sample-rate.
SUMMARY
When converting audio from the analog to the
digital domain, care has to be taken that stop-band
filtering is applied in order to avoid aliasing distortion
in the digital audio signal. Once the signal is converted
to digital, the aliasing distortion products can not be
removed with-out reducing the bandwidth accordingly.
The aliasing distortion will, when the signal is
reproduced on a set of loudspeakers having some IM
distortion, generate AID. Of course good loudspeakers
have lower distortion, but most hi-fi speakers will have
IM distortion thus giving audible AID.
The only way to eliminate the problem with AID is
to apply stop-band filtering on the A/D conversion. If
this is not done AID will cause different problems
depending on the application for the sampled digital
audio signal.
When using 44.1/32 kHz sample-rates, the NF is
close to/within the audible frequency band. This is a
problem for the Compact Disc (CD). Since CDs are
mastered in 44.1 kHz AID is a problem, if the A/D
converters are used without proper filters. If recording
is done with 48 kHz sampling, the Aliasing distortion
will be at frequencies above 20 kHz. This will be a
problem when working with the audio signals in the
sound studio, where the monitored signals will have
AID.
If digital sample-rate conversion is used to generate
the 44.1 kHz master version from 48 kHz source
material, AID will not occur since the alias products
are filtered by the sample rate converter alias filter
assuming of course that a good quality sample-rate
converter is used.
Not many A/D converters are available with NF
stop-band filtering. As mentioned in the abstract, the
majority of converters have 0.45/0.55 anti-alias filters,
which will result in AID. One converter chip is however
available today with NF stop-band filtering, and that
is the CS5397 from Crystal Semiconductors.
This topic of AID and the influence of sampling
bandwidth on the sound quality is something that needs
to be investigated further, since to our knowledge
documented test results are not available. This is
however a subject in which Digital Audio Denmark
will conduct more research in the future.
Digital Audio Denmark A/D converters
The ADDA 2402 A/D, D/A and D/D converter from
Digital Audio Denmark has implemented NF stop-band
filtering for eliminating the risk of AID. This means
that digital recordings can be made without aliasing
distortion. However, a trade-off has to be made
concerning the bandwidth of the sampled signal. When
sampling with 44.1 kHz the transition band starts at
18.1 kHz, and the attenuation at 20 kHz is 12 dB. This
means that the signal 3 dB bandwidth is reduced to
19.3
kHz.
References
[1] R. Blake: “Anti-alias filters: the invisible distortion
mechanism in digital audio”. Preprint 4966, 106
th
AES Convention, Munich 1999.
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