Signal Processing and Communications Laboratory

• University of Cambridge
• Engineering Department
• Information Engineering Division (F)

Digital Audio Restoration - A Statistical Model-Based Approach

by Simon J. Godsill and Peter J. W. Rayner
Introductory site with audio examples

(to accompany the book of the same title.
Copyright: Springer-Verlag London Limited 1998 ISBN 3 540 76222 1.
Address: Sweetapple House, Catteshall Road, Godalming, Surrey, GU7 3DJ)

Full Text now available on line - Download

This document provides an accompaniment to the above text, including audio examples for many of the techniques described in the book. Links are included to various World-wide Web sites, which will not work if you are not connected to the Web, but the main parts of the document are all included on this CD-ROM and can be accessed using any standard Web browser. Simply click on the tracks highlighted in blue to listen to the audio. The track-listing immediately following contains all the processed material in an easily accessible form. The following paragraphs describe the techniques applied in more detail. You will need a .wav-compatible sound card on your machine.

Please contact the authors by email if you find any errors in the text of the book or content of the CD.

We now describe the processing used in each column of the above table.

1. The Source Files (Column 3)

A selection of original source material for restoration. The material ranges from early jazz and classical to modern rock recordings, and the defects range from clicks, pops and crackles to hiss, wow and general pitch defects. All the material is monophonic, but stereo material can be processed channel by channel in a similar manner. All material is sampled and processed at the CD standard of 44.1Khz with 16-bit resolution. Processing is carried out using double precision arithmetic and Matlab-based programs.

2. De-clicked examples (Column 4)

This section demonstrates basic de-clicking as described in chapter 5 of the book. We use a sinusoidal + AR model (see page 111 and 131) for both detection and interpolation of clicks and crackles. A frame length of 2048 samples at 44.1KHz is used, with a 50% overlap between successive frames. Other parameters are tuned to the individual tracks: the AR model order varies between 10 and 40, the number of sinusoids is between 10 and 40, and the detection threshold is between 4 and 8. This model is particularly effective for detecting and removing clicks and crackles with a wide range of amplitudes, as is commonly encountered in early 78rpm records. Of the three extracts processed, two are early jazz recordings (King Oliver (de-clicked), Louis Armstrong (de-clicked)) and one is a more modern classical recording (Mussorsky (de-clicked) ). All of the recordings exhibit a range of click-type defects, with the classical extract being most severely degraded - note the challenging combination of huge `pops' and small crackles. Notice also how the de-clicking procedure manages to eliminate some distortion in the King Oliver recording.

3. Hiss reduction examples (Column 5)

For hiss reduction we present the same two jazz tracks as for de-clicking and a piece of piano music which has been artificially degraded with white Gaussian noise. An FFT-based de-hissing algorithm is used, as described in chapter 6. The processings all use a Wiener-type de-noising rule (p.139). In order to give some insight into the problems of de-hissing, several versions of the piano track are de-hissed in different ways. All processings use a frame length of 2048 samples with 50% overlap, a Hamming window analysis window and Hanning window reconstruction window. The first example (Piano (Musical Noise) ) uses a straightforward implementation of the de-hisser with no modifications, as described on p. 139. You can hear very clearly the effect of `musical' noise (p.141) which makes the processing unusable. The second processing ( Piano (complete noise removal) ) implements some of the improvements suggested on page 145, incorporating temporal information from frame to frame in the processing. We do not detail the precise modifications for reasons of commercial secrecy, but the processing now eliminates all musical noise, leaving a result which sounds unnaturally clean and lacking in `presence'. This can be improved by incorporating a noise floor, and two possible processings are given in Piano (partial noise reduction 1) and Piano (partial noise reduction 2) . Processings using the same method are presented for the two jazz recordings (King Oliver (De-hissed) and (Armstrong (De-hissed)).

It must be re-emphasized that de-hissing is a very subjective procedure and that many other results are possible from these recordings according to taste, performing more or less hiss reduction and achieving different degrees of fidelity to the original recorded sound quality. The CEDAR System uses more sophisticated algorithms still, which allow the remastering engineer to have a greater degree of input and control over the final sound quality. Commercial processings will often include also some re-equalisation of the sound after the de-hissing stage.

4. De-thumped examples (Column 6)

This section includes examples of low frequency noise removal for broken records. The records are literally glued back into one piece before playback and processed using the methods of chapter 7. The first example ( Wagner (de-thumped) ) uses the signal separation method described in section 7.3 and is a challenging track which does not respond very well to simpler methods. The second example ( Squabblin' (de-thumped) ) is somewhat more straightforward and processed using the template methods of section 7.1. Note that both examples have had a light de-clicking process applied following removal of low frequency transients.

5. Correction of pitch variation defects (Column 7)

Here we demonstrate the methods of chapter 8. Two examples of wow correction are given and one of a pitch slide. In the first ( Mendelssohn (de-wowed) ) a second order smoothness prior is used for the wow curve since the wow exhibited no obvious periodicity. In the second ( Sinatra (De-wowed) ), a second order AR model prior was used, with poles placed to correspond to a 78rpm periodicity. Finally a quadratic polynomial model was used to correct the pitch slide in Hadley (pitch corrected).

6. Bayesian sequential click removal (Column 8)

Here we present one example of the Bayesian sequential de-clicking methods described in chapters 9-11 ( Vega (de-clicked) ). The clicks were generated synthetically and added digitally to this modern recording.

7. Bayesian click removal using MCMC (Column 9)

Here a very badly click, crackle and `pop' degraded recording is processed using the MCMC methods of chapter 12: Mozart (de-clicked) .

8. Processings by the CEDAR system (Column 10)

The CEDAR (Computer-enhanced Digital Audio Restoration) system is a commercial system for restoration of degraded recordings of all types. The system allows for real-time click, crackle, hiss, buzz and distortion removal in mono and stereo. The authors were both founding members of the company and are involved in strategic research and consultancy for the company. It should be emphasised that the algorithms and methods described in this book are for research purposes and that the precise techniques employed by CEDAR are not detailed for reasons of commercial secrecy. We present several examples of CEDAR processing to give some idea of what is now routinely achievable in the commercial sphere. These have been processed entirely routinely through the CEDAR-3 real-time system, and as with all of the results presented here represent only one of the many possible output sounds for the tracks concerned: King Oliver (de-clicked and de-hissed), Louis Armstrong (de-clicked and de-hissed), Schubert (de-clicked and de-hissed), Richard Strauss (de-clicked and de-hissed).

9. Commercial processing by Past Perfect and CEDAR (Column 11)

Finally we present an example of commercial processing by the record label Past Perfect, using the CEDAR system and pre-/post equalisation: Formby (de-clicked, de-hissed, equalised).

Work on this book by the first author was partly supported by a grant from the Nuffield Foundation - NUF-NAL

Compiled by Simon Godsill, July 1998

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