44.1 kHz sample rate
Nyquist Frequency
-50
-40
-30
-20
-10
+0
dB
19k
25k
24k
Hz
-60
20k
21k
22k
23k
According to the classic theory on sampling of
analog signals, the spectrum of the signal will be
mirrored round the NF and repeated for each multiplum
of the NF, as shown in Figure 3.
fs/2
fs
2/3 fs
2fs
f/Hz
A/dB
If signal contents are available in the signal above
the NF a mirror of the signal will fold down below the
NF as an alias signal, and thus generate aliasing
distortion. If a broadband signal is sampled with a 0.45/
0.55 anti-alias filter, the spectrum can act as shown in
the example in Figure 4.
fs/2
fs
f/Hz
A/dB
f0
f1
f2
f3
f4
f5
Aliasing distortion
The example shows a signal with a fundamental
frequency of f
0
and a number of harmonics. The 4
th
harmonic is just above the NF, but still in the transition
band of the anti-alias filter of the A/D converter.
INTERMODULATION DISTORTION
Intermodulation distortion is a type of distortion
where non-linearities in the signal path generate
modulation between all the frequency components of
the signal. The primary source for IM distortion in the
audio signal path is the loudspeaker. This is due to the
non-linear behaviour of the speaker cone, which of course
depends on the loudspeaker type and quality.
Modulation means that new frequencies
f
im
are
generated from all positive combinations of two existing
frequencies.
f
im
= |
±
f
1
±
f
2
|
If two frequencies are denominated
f
1
and
f
2
,
where
f
2
> f
1
, and assuming
f
2
< 2f
1
,
the modulation frequencies
generated are as shown in Table 1.
IM distortion will appear up to a very high order,
but third order IM distortion is the highest order that
has any significance in this application. The magnitude
of the modulation products is reduced when the
modulation order rises. The non-shaded areas in the table
are the modulation products with the highest relevance.
IM distortion will generate a-harmonic signals when
aliasing distortion is present, since the alias signal will
modulate with the harmonics of the original signal.
Depending on the frequency contents of the signal
spectrum, some modulation frequencies will be more
audible than others. If an IM frequency is near the
fundamental frequency for the tonal spectrum, the effects
will be quite annoying, unless the IM frequency is within
the masking area, in which case it will not be heard. An
example of IM distortion is shown in Figure 5.
fs/2
f/kHz
A/dB
f0 4,5
f2 13,5
f3 18,0
f4 22,5
Aliasing distortion
f1 9,0
f4’ 21,6
f
4’ -
f
3
f4’ - f3 = 3,6
IM distortion
Figure 5, IM distortion example
Figure 2, Transition band of 0.45/0.55xFS filter
Figure 3, Spectrum of a sampled signal
Figure 4, Aliasing distortion example
When the signal is sampled with an A/D
converter having an anti-alias filter, with stop-band
attenuation at the NF, no aliasing distortion appears.
Table 1, IM frequencies
f
1
f
2
2f
1
3f
1
2f
2
3f
2
f
2
-
f
1
2f
1
-
f
2
3f
1
-
f
2
2f
2
-
2f
1
2f
2
-
2f
1
3f
2
-
2f
1
3f
2
-
f
1
3f
2
-
2f
1
3f
2
-
3f
1
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