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Digital Signal Processing

Digital Signal Processing. Transform Analysis of Linear Time Invariant Systems. Frequency domain study of LTI system. Example: Ideal lowpass filter frequency response. Example: filter frequency response. Frequency and phase response. Example: Pole zero plot and freq response.

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Digital Signal Processing

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  1. Digital Signal Processing Transform Analysis of Linear Time Invariant Systems

  2. Frequency domain study of LTI system

  3. Example: Ideal lowpass filter frequency response

  4. Example: filter frequency response

  5. Frequency and phase response

  6. Example: Pole zero plot and freq response

  7. Rational system function

  8. Stability and Causality • If the ROC contains the unit circle, then the system is stable (its frequency response exists). • If the ROC includes infinity, then the system is causal (a right sided impulse response has a ROC outside a disc, including infinity). • Note: stability and causality are two totally unrelated properties of a system. • A system can be any combination of causal/ non-causal/ stable/unstable. Stability and Causality

  9. ROC

  10. ROC ROC

  11. Stability

  12. Stability Stability

  13. Example: Inverse filter

  14. Frequency response

  15. Group Delay

  16. [H,W] = freqz([1 0 0 0 0 0 0 0 0 0 1], 1, 1024, 'whole'); plot(W/(2*pi), abs(H), 'LineWidth', 4) Matlab allzero

  17. Frequency response

  18. Frequency response of rational system function

  19. Frequency response of rational system function

  20. Frequency response of one zero system

  21. Frequency response of one zero system

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