Digital Signal Processing Reference
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7.7 CONCLUSION
In this contribution a basic introduction into bandwidth extension algorithms for the
enhancement of telephony speech was presented. Since nearly all bandwidth exten-
sion approaches can be split into one part that is generating the required excitation
signal and another part that estimates the wideband vocal tract transfer function, we
have described both tasks in detail in the main body of this chapter.
Even if the resulting quality is not as good as wideband coded speech, significant
improvement (compared to pure transmission over the network) is possible. However,
wideband coding and bandwidth extension are not competitors, since the latter one is
also able to extend even wideband coded speech (e.g. from 7 kHz bandwidth in case of
a transmission according to the ITU standard G.722 17 to 12 or 16 kHz). Due to the
advantage of bandwidth extension schemes to enhance the speech quality of the
incoming signal by bandwidth extension without modifying the network, research
as well as product development in this topic will continue with increasing expense.
7.8 PROBLEMS
In this section we give some exercises that will help the reader to consolidate the tech-
niques learned in this chapter. Attention is drawn to problems that come up when
really designing a system for bandwidth extension. In the following we present the
problems arising using a model based approach for bandwidth extension. The
model based approach is characterized by the two steps of extending the excitation
signal and the extension of the spectral envelope.
7.1
Consider a harmonic signal
p
12
x
(
n
)
¼
cos(3
v
0
n
)
þ
cos(4
v
0
n
) with
v
0
,
in the time domain.
a)
Compute the extended excitation signal
y
(
n
) after the application of a quad-
ratic characteristic to the narrowband excitation signal
x
(
n
).
b)
At what frequencies do now components occur? Do they have equal ampli-
tudes as it was the case with the input signal?
c)
Compute the extended excitation signal
y
(
n
) after the application of a cubic
characteristic to the narrowband excitation signal
x
(
n
).
d)
At what frequencies do now components occur?
e)
Assume a harmonic excitation signal sampled at 8 kHz with a fundamental
frequency of 150 Hz which has been limited by a lowpass filter with a
cutoff frequency of 3400 Hz. What problems occur if a quadratic character-
istic is applied to extend the harmonics? What can be done against these
effects?
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