BANDWIDTH EXTENSION OF TELEPHONY SPEECH - Adaptive Signal Processing: Next Generation Solutions - page 383

Concluding Remarks We have mentioned only the very basic approaches in
this section and we do not claim for completeness. Several important approaches,
such as Gaussian mixture models (GMMs) or mapping matrixes that operate directly
on DFT-based input vectors, have not been treated. For these approaches we refer to
topics and Ph.D theses such as [15] or [20, 24].

7.6 EVALUATION OF BANDWIDTH EXTENSION ALGORITHMS

In many situations and particularly in the context of developing and improving band-
width extension algorithms, performance measures are needed for comparison
between different versions of a particular algorithm or different algorithms.
Bandwidth extension systems are often evaluated utilizing objective measures, such
as distance measures [12, 14] between the original broadband and the extended
signal. These measures can be quantified in straightforward objective terms. We
will describe a few of them in the next section. However, due to the complexity of
current algorithms these methods deliver only a general sense of the speech quality.
A better, but also more expensive, way to evaluate the speech quality are subjective
listening tests. These tests are the most reliable tool available for the evaluation of
bandwidth extension algorithms. The challenge of these tests is to design them in
such a way that the quality of the extension system can be measured in a reliable
and repeatable manner. A variety of listening test have been published, each of
them optimized for a special purpose. We will focus here only on comparison mean
opinion scores (CMOS). For this kind of subjective test standards have been published
by the International Telecommunication Union (ITU) [18]. 8

7.6.1 Objective Distance Measures

Some well known objective distance measures are L 2 -norm based logarithmic spectral
distortion measures [12], such as

ð

p

2

10 log 10 j S ext ( e jV , n ) j

2

1
2 p

d Eu,log ( n ) ¼ dV: (7 : 58)

2

jS bb ( e jV , n ) j

p

Here S ext ( e j V , n ) denotes the short-term spectrum of the bandwidth extended
signal and S bb ( e jV , n ) is the original broadband spectrum. In order to achieve a
reliable measurement, the distances d Eu,log ( n ) between the original and the estimated

8 Note, that the reason why we focus here only on the speech quality and not on the speech intelligibility
using, for example, diagnostic rhyme tests [2, 37] is because of the nature of bandwidth extension algor-
ithms. Even if a bandwidth extension system increases the bandwidth and makes the speech sound better
it does not add any new information to the signal.