Distortion Effects from Aliasing in Digital Audio
Mikael Vest and Peter Scheelke
Digital Audio Denmark
www.digitalaudio.dk
ABSTRACT
When converting audio between the analog and digital audio domains, the well-known effects from alias signals have
to be taken into consideration. Generally, audio converters do not have adequate filtering to eliminate this kind of
spectral distortion. During recent works it has been concluded that the sound quality of digital recordings can be drastically
improved when applying efficient stop-band filtering.
INTRODUCTION
When converting an analog signal to a digital
signal, the analog signal is sampled with a frequency
of twice the bandwidth that is required for the digital
representation. To get an optimal sampling, the
bandwidth of the analog signal must not exceed half
the sampling frequency, also referred to as the Nyquist
frequency (NF). If frequency contents are present above
the NF, a mirror of the frequencies is generated at
frequencies symmetrical to the NF and new frequencies
are thus generated with no harmonic relationship to
the tonal contents of the original signal. This
phenomenon is referred to as aliasing distortion. If the
distortion is only present at high frequencies, it is not
likely that it can be heard, and therefore it will not
degrade the signal quality. However, when the digital
signal has to be reproduced using D/A coverters,
amplifiers and indeed analog transducers such as
loudspeakers will introduce intermodulation distortion
(IMD) to the signal. IMD means that the frequencies
of the signal mix together and generate new
frequencies, which can be audiable if the distortion
exceeds certain levels. The problem is now that when
new a-tonal frequencies are added to the signal due to
aliasing distortion, such signals will mix very badly
with the rest of the program and thus be audiable.
The important fact of this problem is that
distortion happens when the signal has both aliasing
distortion and IMD above a certain level. Of course, it
depends on the quality of the sampling and the quality
of the reproduction equipment, and in particular the
loudspeakers. This effect is referred to as Aliasing
Intermodulation Distortion (AID).
Over the years discussions and papers on sound
quality of digital recorded material have been many.
However, at the 106
th
AES Convention in Munich a new
thesis was presented by Mr. Richard Black [1] stating
the problems of this combined distortion phenomenon.
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44.1 kHz sample rate
48 kHz sample rate
Nyquist Frequency
In the case of FS = 44,1 kHz, the stop-band will
only be effective at 24,26 kHz, and the attenuation at
the NF is approx. 8.5 dB. In Figure 2 a close-up of the
transition band frequency response is shown.
Figure 1, Frequency response of 0.45/0.55xFS filter
Today high quality audio A/D converters are
typically based on the delta-sigma conversion
principle with 64/128 times over sampling and
internal digital filtering. According to the
manufacturers of the converter chipset, this removes
the need for an external anti-alias filter. However the
filters normally implemented are so called 0.45/0.55
times the sample frequency (FS) filters. This means
that the pass band goes to 0.45xFS, and the stop-band
starts from 0.55xFS. In Figure 1 the frequency
response is shown with 44.1 kHz and 48 kHz sample
frequency.
This paper has the purpose of explaining the
basis of this distortion type, which he had recently
identified.
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Figure 1, Frequency response of 0.45/0.55xFS filter
