1. Introduction to Digital Systems Saint-Petersburg State University Faculty of Applied Mathematics – Control Processes Lections 2 ─ 4 prof. Evgeny I. Veremey 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. 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 of DLTI systems First Backward Finite Difference

8. Models of DLTI systems 7 Basic model of DLTI system with one input and one output (SISO DLTI) Linear Non-homogeneous Difference Equation

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

10. Models of DLTI systems 9 DIGITAL FILTERS ARMA AR MA – Recursive Digital Filters FIR Filters – Non-recursive Digital 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 1212 № 1. 2. 3. 4. 5. 6.

14. Models of DLTI systems 1313 Unilateral (One-Side) Z-Transformation

15. Models of DLTI systems 1414 Reverse Z-Transformation

16. Models of DLTI systems 15 Reverse Z-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