Notes by a friend for Signals II (DSP Fundamentals) - 5ESC0
- Topics: Z-Transform
Definition:
Generalization of Discrete Fourier Analysis (friend) - 5ESC0
Properties:
- Continuous counterpart: Laplace Transform (friend) - 5ESC0
- Relation to Discrete Fourier Analysis (friend) - 5ESC0:
- Radius of convergence (ROC):
- Consists of rings centered at origin in z-plane
converges ROC includes unit circle finite → ROC is entire z-plane (exception of z=0 | z= ) right-sided → ROC circularly right-sided left-sided → ROC circularly left-sided
- Causality:
poles >= zeros, right-sided (ROC contains due to IVT) - Stability: ROC includes unit circle
- Realizability: causal + stable → all poles inside unit circle
