O.I. Berngardt, A.V.Djourik
Institute of Solar-Terrestrial physics SD RAS, 126, Lermontova Str., 664033, Irkutsk, Russia

Abstract
A mathematical algorithm is suggested and realized, that determines authenticity of a musical compact-disc using the character of the audiodata it contains, and predicts its possible source  is it an original record or a reconstruction from a lossy encoded music file (for example, MP3). The algorithm is based on the analysis of the Fourier-spectra of the signal time segments during all the record and on the calculation of the character bound frequency on every time segment. Based on the analysis of spectral statistical properties and on a number of criteria, the source of the audiorecord is determined  if it is an original or lossy encoded audio file. The testing is carried out using both modern and old records of poor quality. It has shown a good accuracy of the algorithm, which differentiates original records and that reconstructed from lossy encoded data.

Project description

It is no secret that the Internet and file-exchanging networks are literally overloaded with music. The plenty of various formats which compress music files just favours this situation. Files in formats with lossy encoding and the highest degree of compression, like MP3, have got the greatest prevalence. While playing such files using cheap acoustic systems one can hardly distinguish their dissimilarity from the original ones, but all the distortions become evident when listening such disks on a Hi-Fi systems or using stereo headphones, especially if one has an opportunity to compare a record with its original. That is why when purchasing musical compact-discs a question always arises: whether the disc is a pirate fake or not. To answer this question, spectral characteristics of the signal can be used, because in contrast to the original records, the lossy algorithms significantly distort the spectral characteristics of the signal.
The suggested algorithm of the record authentity is the following:

1. One music channel is read sequently.
2. On each time segment a logarithm of the spectral power [1] with small additive constant is calculated. A small constant is used to exclude the logarithm calculation error.
3. A scatter of the logarithm of the spectrum values is calculated. The maximum frequency on which scatter sharply increases is considered to be a bound one, that corresponds to a maximum character frequency in the audio signal spectrum, that is not connected with numerical or statistical noise [2]. here is scatter of the values in the frequency interval .
4. Based on the statistical distribution of the bound frequencies the two character frequencies are determined  average bound frequency and most probable bound frequency.

• A.L.Webber, Sunset boulevard (1993, The Really useful Group Ltd., PolyGram Records)
• A.L.Webber, Phantom of the opera (1987, The Really useful Group Ltd., EMI studios)
• A.L.Webber, Cats (1983, The Really useful Group Ltd., PolyGram Records)
• Feodor Shaljapin (anthology of russian variety, the beginning of 20 century, the Center of Revival and Propaganda of the Historical and Cultural Heritage of the fatherland)
• Luis Armstrong, I got rhythm (Tring International PLC)
• Mendelsohn, Violin concerto (1994, Elap Music A/S)
• Schumann, Piano concerto (1994, Elap Music A/S)
• Liszt, Piano concertos (1994, Elap Music A/S)
• Samkha & Friends, Piligrim (2003, Landy Star Music & Elektrus)
• EURO DJ HITS, 2003 (2003, JJRecords)
• E.L.O. De Luxe collection (Dream Sound Studio)
• Sting, The soul cages (1991, A&M Records Inc.)
• Boris Grebenshikov, Radio Silence (1996, Triarius)