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Introduction to Digital Systems: Mathematical Models and DLTI Systems

This lecture series by Prof. Evgeny I. Veremey at Saint-Petersburg State University covers the fundamental concepts of digital systems, focusing on Mathematical Models of Discrete Linear Time-Invariant (DLTI) systems. It includes topics such as Linear Transformations of Discrete Signals, Discrete Convolution, and Difference Equations. The series also explores Auto-Regressive and Moving Average models, Recursive and Non-recursive Digital Filters, and various Z-Transformation techniques. This foundational knowledge is essential for control processes in applied mathematics.

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Introduction to Digital Systems: Mathematical Models and DLTI Systems

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  1. Introduction to Digital Systems Saint-Petersburg State University Faculty of Applied Mathematics – Control Processes prof. Evgeny I. Veremey Lections 2 ─ 4 Part 1. Mathematical models of Digital Systems

  2. Models of DLTI systems 1 1. Linear Transformations of Discrete signals

  3. Models of DLTI systems 2

  4. Models of DLTI systems 3 Unit discrete impulse, shifted impulse

  5. Models of DLTI systems 4 Discrete Convolution

  6. Models of DLTI systems 5 Three steps to construct impulse response sequence h[n-k]

  7. Models of DLTI systems 6 2. Difference Equation Models ofDLTIsystems First BackwardFiniteDifference

  8. Models of DLTI systems 7 Basic model ofDLTI system withone inputandone output (SISO DLTI) LinearNon-homogeneousDifference Equation

  9. Models of DLTI systems 8 Various Kindsof SISO DLTI Models Auto-Regressive Moving Average (ARMA) Model Auto-Regressive (AR) Model Moving Average (MA) Model

  10. Models of DLTI systems 9 DIGITALFILTERS ARMA – Recursive DigitalFilters AR – Non-recursive DigitalFilters MA FIR Filters

  11. Models of DLTI systems 10 State Space Difference Equations of DLTI systems AR Model

  12. Models of DLTI systems 11 3. Z -Transformation (Laurent Transformation) Direct Bilateral (Two-side) Z-Transformation

  13. Models of DLTI systems 12

  14. Models of DLTI systems 13 Unilateral (One-Side)Z-Transformation

  15. Models of DLTI systems 14 ReverseZ-Transformation

  16. Models of DLTI systems 15 ReverseZ-Transformation for Rational Functions

  17. Models of DLTI systems 16 Solution of the Difference Equations in z-Domain

  18. Models of DLTI systems 17 4. DLTI Systems Models in z-Domain TRANSFER MATRIX:

  19. Models of DLTI systems 18 Transfer Functions of Digital Filters Filter Transfer Function

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