**DSP Algorithms and Discrete Transforms**

296 Applications of Digital Signal Processing

Hoefkens, J.; Berz, M. & Makino, K. (2001), *Verified High-Order Integration of DAEs and* 

Hoefkens, J.; Berz, M. & Makino, K. (2003), "Controlling the Wrapping Effect in the Solution

Kaucher, E. (1980), "Interval Analysis in the Extended Interval Space IR", *Computing Suppl.*,

Lemke, A.; Hedrich, L. & Barke, E. (Nov. 2002), *Analog Circuit Sizing Based on Formal Methods* 

López, J.A. (2004), *Evaluación de los Efectos de Cuantificación en las Estructuras de Filtros* 

López, J.A.; Carreras, C. & Nieto-Taladriz O. (2007), Improved Interval-Based

Makino, K. (1999), "Efficient Control of the Dependency Problem Based on Taylor Model

Makino, K. & Berz, M. (1999), "COSY INFINITY Version 8", *Nuclear Instruments and Methods*,

Makino, K. & Berz, M. (2003), "Taylor Models and Other Validated Functional Inclusion

Ortolf, J. H. (Bonn, 1969), "Eine Verallgemeinerung der Intervallarithmetik", *Geselschaft fuer* 

Shou, H.; Lin, H.; Martin, R. & Wang, G. (2003), "Modified Affine Arithmetic Is More

Walster, G. W. (2004), *G.W. Walster Papers, http://www.mscs.mu.edu/globsol/walster-papers.html.* 

Accurate than Centered Interval Arithmetic or Affine Arithmetic", *Mathematics of Surfaces, 10th IMA International Conference, Proceedings*, 2768 / 2003, 355 - 365. Shou, H.; Martin, R.; Voiculescu, I.; Bowyer, A. & Wang, G. (2002), "Affine Arithmetic in

Matrix Form for Polynomial Evaluation and Algebraic Curve Drawing", *Progress in* 

Moore, R. E. (1962), *Interval Arithmetic and Automatic Error Analysis in Digital Computing*,

Makino, K. (1998), *Rigurous Analysis of Nonlinear Motion in Particle Accelerators*,

Methods", *Int. J. of Pure and Applied Mathematics*, 4, 4, 379-456.

Neumaier, A. (2002), "Taylor Forms, Use and Limits", *Reliable Computing*, 9, 43-79.

SIGLA/X (1999b), *Applications of Interval Analysis to Systems and Control*, 127-227. Stolfi, J. & Figuereido, L. H. d. (1997), *Self-Validated Numerical Methods and Applications*.

Tupper, J. A. (1996), *Graphing Equations with Generalized Interval Arithmetic*. Vehí, J. (1998), *Anàlisi i Disseny de Controladors Robustos Mitjançant Interval Modals*,

http://www.engr.wisc.edu/ece/faculty/ schulte\_michael.html

*Digitales Utilizando Técnicas de Cuantificación Basadas en Extensiones de Intervalos*,

Characterization of Fixed-Point LTI Systems With Feedback Loops, *IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems,* vol. 26, pp. 1923-1933. López, J.A.; Caffarena, G.; Carreras, C. & Nieto-Taladriz O. (2008), Fast and accurate

computation of the roundoff noise of linear time-invariant systems, *IET Circuits,* 

Kearfott, R. B. (2004), *R.B. Kearfott Homepage*. http://interval.louisiana.edu/kearfott.html Kreinovich, V. (2004), *The Interval Computations Homepage*. http://www.cs.utep.edu/

Hoefkens, J. (2001), *Verified Methods for Differential Algebraic Equations*.

of ODEs of Asteriods", *Reliable Computing*, 9, 1, 21-41.

Ph.D. Thesis, Univ. Politécnica de Madrid.

*Devices & Systems*, vol. 2, pp. 393-408.

Methods", *Reliable Computing*, 5, 1, 3-12.

Neumaier, A. (1990), *Interval Methods for Systems of Equations*.

*Mathematik und Datenverarbeitung*, 11, 1-71. Schichl, H. & Neumaier, A. (2002), *Interval Analysis – Basics*.

Moore, R. E. (1966), *Interval analysis*, Prentice-Hall.

Schulte, M. J. (2004), *M.J. Schulte Homepage*.

*Natural Science*, 12, 1, 77-81.

SIGLA/X (1999a), *Ground Construction of Modal Intervals*.

*Higher-Order ODEs*, 281-292.

2, 33-49.

interval-comp/

A427, 338-343.

*Using Affine Arithmetic*.

**14** 

*Russia* 

**Digital Camera Identification** 

*Technological Institute of Southern Federal University* 

Dmitry Rublev, Vladimir Fedorov and Oleg Makarevich

The development of instruments for copyright protection and pirated copies detection requires new methods of intellectual property protection. Specific of execution of that analysis considerably depends on media type — whether it material or energy and

To analyse the capability of identification due to direct dependence of ID-procedure on media nature it is feasible to select two groups of media: material (physical bodies) and energetical (physical fields: electric currents, sound fields, etc). The common property of any field is wavelike pattern so it can be named wave media type. Electric current both the power carrier and an media. On the material media the information if fixed by changing physical properties according to character alphabet. Information transfer by material media is done by transfer of changed matter. Information fixation by wavelike media is done by environmental changes. Information transfer by wavelike media is performed by energy transfer. According to abovementioned, the analog recording device identification (for example microcassette dictophone) is done by traces leaved on by material media by on-off impulses, transients, inactivity noises, noise of clear media (magnetic tape), high-frequency current for magnetic bias, speed parameters of deck. For analog cameras that type of parameters includes frame margin, film-feeding and optical system specific features. For printers this type of parameters includes features of methods and alogorithms of rasterizing

Devices which uses energy media are also identifiable, for example radio transmitting

Easy bit-to-bit copying process of digital information and inapplicability of traditional "original vs copy" division both with non availability of automated procedures of digital sourcing had led to wide distribution of counterfeit production. Identification based on format features, metadata fields, etc is unreliable because of its removal and forgery simplicity. Use of digital watermarks for content protection is not always possible due to

**1. Introduction** 

**1.1 Identification task** 

recording device (analog or digital).

amd printing methods implementation.

**1.2 Digital recording identification features** 

computational complexity of embedding procedure.

devices are identified by transients of modulated signal.

**Based on Original Images** 
