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Introduction to Digital Systems

Introduction to Digital Systems. Saint-Petersburg State University Faculty of Applied Mathematics – Control Processes. prof. Evgeny I. Veremey. Lections 13 ─ 16. Part 3. Analog System Discretization. Analog Systems Discretization. 1. 1. The signals sampling. Sampling frequency:.

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Introduction to Digital 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 13 ─ 16 Part 3. Analog System Discretization

  2. Analog Systems Discretization 1 1. The signals sampling Sampling frequency: Sampling Period: Example:

  3. Analog Systems Discretization 2 Uncertainties of the analog signal restoration Zero order hold and first order hold restoration

  4. Analog Systems Discretization 3 The sampling of harmonic continues-time functions

  5. Analog Systems Discretization 4 The sampling of harmonic continues-time functions Frequencies are not comparable: Frequencies are comparable:

  6. Analog Systems Discretization 5 The aliasing effect

  7. Analog Systems Discretization 6 2. The base conceptions of analog systems discretization Analog system: Approximate calculation of the definite integral Direct Euler method: Inverse Euler method: Trapezium method:

  8. Analog Systems Discretization 7 Direct Euler method: Inverse Euler method: 3. Discretization methods for the analog LTI systems Cauchy formula:

  9. Analog Systems Discretization 8 Cauchy formula: Matrix exponent: Discrete Analog Approximate ADM Precise PDM

  10. Analog Systems Discretization 9 Analog-digital matrices correspondence: Nonsingular matrix A:

  11. Analog Systems Discretization 10 Two ways for approximate discretization: 1. Taylor approximation 2. Pade approximation Direct Euler method:

  12. Analog Systems Discretization 11 Inverse Euler method (Pade m=0, l=1): Trapezium method (Pade m=1, l=1):

  13. Analog Systems Discretization 12 4. Тhe precise discretization taking into account input signal waveform LTI discretization with preliminary ZOH: Case 1. δ-functions sequence:

  14. Analog Systems Discretization 13 4. Тhe precise discretization taking into account input signal waveform LTI discretization with preliminary ZOH: Case 1: δ-functions sequence:

  15. Analog Systems Discretization 14 Case 2: piecewise constant input signal: Nonsingular matrix A: MATLAB implementation:

  16. Analog Systems Discretization 15 Case 3: piecewise exponential input signal: Case 4: sequence of rectangular impulses:

  17. Analog Systems Discretization 16 5. Тhe precise discretization of LTI systems with tf-models LTI discretization with preliminary ZOH:

  18. Analog Systems Discretization 17

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