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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 Transform Analysis of Linear Time Invariant Systems
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
ROC ROC
Stability Stability
[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