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high frequency components from low is required, since any low-level high frequency
information in the noisy recorded signal is likely to be buried deep in noise. Such
a process becomes highly subjective, since different instruments will have different
high frequency characteristics. The procedure may thus be regarded more as signal
enhancement than restoration.
Pitch adjustment will be required when a source has been played back at a different
(constant) speed from that at which it was recorded. This is distinct from wow (see
section 4.6) in which pitch varies continuously with time. Correction of this defect can
often be made at the analogue playback stage, but digital correction is possible through
use of sample-rate conversion technology (see section 4.6). Time-scale modification
(see the chapter by Laroche) is not required, since changes of playback speed lead to
a corresponding time compression/expansion. We note that correction of this defect
will often be a subjective matter, since the original pitch of the recording may not be
known exactly (especially in the case of early recordings).
recent work in this field [Troughton and Godsill, 1997] applies Bayesian Markov chain
Monte Carlo (MCMC) methods to the problem of non-linear model term selection. It
is planned to extend this work in the near future to model selection for the AR-NAR
distortion models discussed earlier in this section.
4.8
OTHER AREAS
In addition to the specific areas of restoration considered in previous sections there are
many other possibilities which we do not have space here to address in detail. These
include processing of stereo signals, processing of multiple copies of mono recordings,
frequency range restoration and pitch adjustment.
Where stereo signals are processed, it is clearly possible to treat each channel as
a separate mono source, to which many of the above processes could be applied (al-
though correction of pitch variations would need careful synchronization!). However,
this is sub-optimal, owing to the significant degree of redundancy and the largely un-
correlated nature of the noise sources between channels. It is likely that a significantly
improved performance could be achieved if these factors were utilized by a restoration
system. This might be done by modelling cross-channel transfer functions, a difficult
process, owing to complex source modelling effects involving room acoustics. Initial
investigations have shown some promise, and this may prove to be a useful topic of
further research.
A related problem is that of processing multiple copies of the same recording. Once
again, the uncorrelated nature of the noise in each copy may lead to an improved
restoration, and the signal components will be closely related. In the simplest case, a
stereo recording is made from a mono source. Much of the noise in the two channels
may well be uncorrelated, in particular small impulsive-type disturbances which affect
only one channel of the playback system. Multi-channel processing techniques can then
be applied to extraction of the signal from the noisy sources. A Bayesian approach to
this problem, which involves simple FIR modelling of cross-channel transfer functions,
is described in [Godsill, 1993], while a joint AR-modelling approach is presented in
[Hicks and Godsill, 1994]. In the case where sources come from different records,
alignment becomes a major consideration. Vaseghi and Rayner [Vaseghi and Rayner,
1988, Vaseghi, 1988, Vaseghi and Rayner, 1989] use an adaptive filtering system for
this purpose in a dual-channel de-noising application.
In many cases the frequency response of the recording equipment is highly in-
adequate. Acoustic recording horns, for example, exhibit unpleasant resonances at
mid-range frequencies, while most early recordings have very poor high frequency
response. In the case of recording resonances, these may be identified and corrected
using a cascaded system model of source and recording apparatus. Such an approach
was investigated by Spenser and Rayner [Spenser and Rayner, 1989, Spenser, 1990].
In the case where high frequency response is lacking, a model which can predict
4.9
CONCLUSION AND FUTURE TRENDS
This Chapter has attempted to give a broad coverage of the main areas of work in
audio restoration. Where a number of different techniques exist, as in the case of click
removal or noise reduction, a brief descriptive coverage of all methods is given, with
more detailed attention given to a small number of methods which the authors feel to
be of historical importance or of potential use in future research. In reviewing existing
work we point out areas where further developments and research might give new
insight and improved performance.
It should be clear from the text that fast and effective methods are now available
for restoration of the major classes of defect (in particular click removal and noise
reduction). These will generally run in real-time on readily available DSP hardware,
which has allowed for strong commercial exploitation by companies such as CEDAR
Audio Ltd. in England and the American-based Sonic Solutions in California. It
seems to the authors that the way ahead in audio restoration will be at the high
quality end of the market, and in developing new methods which address some of
the more complex problems in audio, such as correction of non-linear effects (see
section 4.7). In audio processing, particularly for classical music signals, fidelity of
results to the original
perceived
sound is of utmost importance. This is much more
the case than, say, in speech enhancement applications, where criteria are based on
factors such as intelligibility. In order to achieve significant improvements in high
quality sound restoration sophisticated algorithms will be required, based on more
realistic modelling frameworks. The new models must take into account the physical
properties of the noise degradation process as well as the psychoacousical properties
of the human auditory system. Such frameworks will typically not give analytic results
for restoration, as can be seen even for the statistical click removal work outlined in
