1. Digital Systems of Control and Signal Processing Saint-Petersburg University Faculty of Applied Mathematics – Control Processes Introduction and Course Content Evgeny I. Veremey, Professor Margarita Sotnikova, Senior Lecturer, PhD

2. CBU Winter School in Information Technology Saint Petersburg, 27 January - 5 February 2011 Introduction to digital systems of control and signal processing General Preface Course 1. "Digital systems of control and signal processing" Prof. E. Veremey, Senior Lecturer M. Sotnikova, SPbU, Russia Course 2. “Computer graphics and image processing" Assoc. Prof. I. Makeev, SPbU, Russia Course 2. “Image Compression" Assist. Prof. A. Kolesnikov, University of Eastern Finland

3. Peter the Great's ukase (edict) regarding the foundation of a university in St. Petersburg was approved by the Senate of the Russian Empire on 28 January 1724. A characteristic feature of this, Russia's first, institution of higher education was its organic link with the other two constituents of St. Petersburg's scholastic trinity: the Academy of Sciences and the Grammar School.

4. University today: Today St Petersburg State University is a major Russian center of science, education and culture of international repute. Many important universities in Europe, America, and Asia - notably Cambridge University (UK), Bologna University (Italy), the Free University of Berlin and Hamburg University (Germany), Carlton University (Canada), Amsterdam University (the Netherlands), Stockholm University (Sweden), the Municipal University of Osaka (Japan), to name but a few, - have maintained various academic contacts with the University of St. Petersburg. The discoveries and achievements of the University professors and graduates have become part of the history of both international and Russian science and technology. Eight of them were awarded Nobel Prizes - I.Pavlov (1904) and I.Mechnikov (1908) for physiology and medicine; N.Semenov (1956) for chemistry; L.Landau (1962) and A.Prokhorov (1964) for physics; V.Leontyev (1973) and L.Kantorovich (1975) for economics, I.Brodsky (1985) for literature. 21 faculties - 11 Scientific Institutes - Academicals School - over 25.000 students - near 2.000 Postgraduate students - near 5.000 lecturers & researchers - over 40 members of Russian Academies of Science, Education etc.

5. The Faculty of Applied Mathematics and Control Processes is Russia's first faculty in this field. It was opened in 1969 on the several departments base of Mathematics and Mechanics Faculty, as well as a few laboratories belonging to the Research Institute of Mathematics and Mechanics of Leningrad University. In their teaching and research the staff draw on the rich traditions of the St Petersburg-Leningrad mathematics school, which is connected with such world- famous names as L.Euler, P.Chebyshev, A.Liapunov, A.Markov, and others. The Faculty is a major training and research center capable to solve any scientific problems involving the use of computer-based technologies and the training or retraining of professionals in this field. The Faculty graduates are fully qualified to work successfully in any sphere that requires the use of applied mathematics and computer science. Today, this sphere extends to practically every kind of human activity - from defense and high tech down to biology, management, ecology, finance, economics, and communications. 1500 students – 100 post graduators (PhD students) – 250 educational and research staff (40 Doctors of science, 90 PhD) – 20 departments – 9 scientific laboratories – 5 teaching laboratories AMPC Faculty of SPbU

6. Educational directions for graduators: Applied Mathematics & Informatics Applied Mathematics & Physics, Informational Technologies Educational programs: 4-year bachelor studying 2-year master studying 5-year specialist studying Educational directions for post graduators (PhD students): - Automation of Production & Technological Processes - Automation & Software for Computers, Computer Complexes, Systems & Networks - Computational Mathematics - Differential Equations - Mathematical Cybernetics - Mechanics of Deformed Solids - Systems for Automated Design - Computers Application, Mathematical Modeling & Methods in Research AMPC Faculty of SPbU

7. Educational activities: The faculty is engaged in fundamental research. The results are regularly published in the leading national and international scientific journals, are reported on the international workshops, conferences and congresses. The list of scientific books published by the Faculty staff members exceeds 500 titles. Starting from 1969 more than 500 Ph. D. and about 100 Dr. Sci. dissertations were prepared and defended. Many different scientific enterprises are under way. The applications selected for study frequently have nonstandard features that, in turn, leads to creation of new mathematical methods and tools. The area of particular interest has always been the control theory with its various applications. The research and educational programs are administered through the structure of departments and laboratories. A number of seminars support the research activities. It has become a tradition of the faculty to carry out regular weekly seminars in the Theory of Control, Game Theory, Numerical Analysis, Problems of the Deformable Solid Mechanics and others. The educational process is based on the best traditions of St.Petersburg mathematical school, inspired by such well-known mathematicians as L.Euler, P.L.Chebyshev, A.M.Lyapunov, A.A.Markov and many others. AMPC Faculty of SPbU

8. Curriculum (general obligatory courses): Mathematical Analysis Higher Algebra Geometry Complex Analysis Differential and Integral Equations Calculus of Variations Mathematical Programming Mathematical Physics Numerical Analysis Control Theory Game Theory and Operations Research Probability Theory and Mathematical Statistics Mechanics of the Controlled Motion Deformed Solid Mechanics Computers and Programming Languages Informational Logical Systems Control Models AMPC Faculty of SPbU

9. Some Photos of our everyday life

17. Content of the Course 1 Part 1. MATHEMATICAL MODELS of DIGITAL SYSTEMS 1. Linear transformation of digital signals 2. Mathematical Models of DLTI systems on the base of difference equations Z-transformation (Laurent transformation) 3. Z-transformation (Laurent transformation) INTRODUCTION 1. The Discrete Time Fourier series and Transformation 2. The Discrete Fourier Transformation Frequency responses of DLTI systems 3. Frequency responses of DLTI systems Part 2. ANALISYS OF DIGITAL SIGNALS and SYSTEMS 4. Mathematical models of DLTI systems in z-domain Stability of DLTI systems 4. Stability of DLTI systems Performance Indices of Digital Systems 5. Performance Indices of Digital Systems

18. Content of the Course 1 Part 3. SYNTHESIS of DIGITAL SYSTEMS 2. Parametrical optimization with given admissible dynamical region 3. Modal approach to the synthesis 4. Optimal LQR synthesis 1. Оptimization approach to digital systems analysis and design

19. Cart fixed by the spring 2

20. Controlled cart 3 - output of sensor Methods of control а) by disturbance б) by output Program Control Feedback :

21. Controlled cart 3 Coding of Analog Signal а) initial analog signal б) result of filtering в) digital sygnal

22. Digital Processing of Analog Signal 6 Processing Scheme

23. Controlled cart 7 Encoding of Digital Signal a) digital signal b) result of D/A c) result of smoothing