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From: max@trinity.uucp (Max Hauser)
Newsgroups: rec.audio,sci.electronics
Subject: Re: Restoration
Summary: Homomorphic and adaptive filtering; dynamic time warping
Message-ID: <4493@pasteur.Berkeley.Edu>
Date: 15 Jul 88 22:27:17 GMT
References: <4944@husc6.harvard.edu> <2266@pt.cs.cmu.edu>
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Reply-To: max@eros.berkeley.edu (Max Hauser)
Organization: UC Berkeley
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In article <2266@pt.cs.cmu.edu>, Paul Dietz wrote:

| In article <4944@husc6.harvard.edu> ... (Paul Gallagher) writes:
| >Why isn't it possible to completely restore a recording: for example, to remove
| >all extraneous noise (hiss, clicks, coughs), even to make a reasonable guess
| >about information not in the original recording (for example, given a score
| >and a knowledge of the harmonics of a voice or an instrument, to recreate
| >something close to the sound of the original performance)?
| 
| Actually, this sort of thing is commonly done. 

I'm not sure that I would concur with this.  People frequently suggest 
strategies similar to Paul Gallagher's, above; but the problem arises in
translating ideas like "knowledge of harmonics of a voice or an instrument"
into hard specifics, algorithms that act on the recorded information,
to do the job.  The obstacles are not in the broad concept but in the
nitty gritty.

| I remember hearing a story
| about some Caruso recordings that were restored by having a singer
| imitate as closely as possible the original, and then using this to
| generate optimal filters that were then applied to the original recordings.

Stockham at Utah, pioneering the use of serious DSP in digital audio,
used a blind deconvolution algorithm fifteen years ago to separate Caruso's
"original" voice from the severely (but linearly) distorting acoustics 
of the cylinder phonograph system that recorded him.  Blind deconvolution
is the process of recovering an original signal from a filtered version of
it without knowing what filter was used; it works when the filter and the
original signal have characteristic natural frequencies (or singularities)
in distinct regimes of frequency.  The particular algorithm in this case was
a form of homomorphic filtering [1], which is a practical example of a real
tool that can help implement the regrettably inexact idea of "separating 
desired from undesired" signals.  Stockham, BTW, formed a firm, now 
DRC-Soundstream I believe, and commercialized the method.  People who have
heard the deconvolved Caruso asserted to me that the corrupted original 
sounded better, to their ears (whether because of second-order defects in
the process or because Caruso was phonogenic, I won't presume to guess).

It may not have been the same case that Paul Dietz was referring to.

| I suggest you look at the literature on adaptive filtering. Widrow and
| Stearns "Adaptive Signal Processing" in the Prentice-Hall Signal
| Processing Series is a good place to start.

I agree with this.  Unfortunately, classical (Widrow-type LMS-linear)
"adaptive" filtering, while it is another very useful tool with a lot of 
applications, really addresses a different class of problems from what 
Paul Gallagher proposed.  They tend to be applications that can be cast in
the form of training a device (the adaptive filter) to give a precisely 
known output, or to eliminate an interfering signal that is mathematically
degenerate in some way (e.g., is narrowband) or is available in some 
distorted form itself.  Again, in every case you need a mathematical, not
just an intuitive, basis for attacking the problem.

Another basic tool that might have relevance here is dynamic time
warping (DTW), used routinely in applications like pattern recognition
where inputs (like speech) are subject to uncontrollable time-scale
expansions and compressions.  Unlike the classes of algorithms mentioned
so far, DTW doesn't assume rigid time alignment among the different
signals being manipulated and compared.  I just mention it.  I wish 
someone with a broad background would attack the problem that Paul 
Gallagher raised, or at least summarize in the literature the different
tools that are steps in that direction.  Perhaps it has been done --
if so, please post.  The different tools, characteristically, arise in
very different fields of inquiry, hence the need for broad background.

[1] Oppenheim and Schafer, _Digital Signal Processing_, Prentice-Hall
1975, Chapter 10, is a broad introduction to homomorphic sig. proc.

Max Hauser / max@eros.berkeley.edu / ...{!decvax}!ucbvax!eros!max