s-Plane (Complex Plane)
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Time Domain Response f(t)
Mathematical Decomposition (Partial Fractions)
Add poles/zeros to see the exact time-domain equation...
Intuition Guide:
σ (Real axis) controls exponential Decay / Growth.
jω (Imag axis) controls Oscillation Frequency.
ROC (Region of Convergence) must include the jω axis for a stable, causal system.
σ (Real axis) controls exponential Decay / Growth.
jω (Imag axis) controls Oscillation Frequency.
ROC (Region of Convergence) must include the jω axis for a stable, causal system.
Frequency Response (Bode Magnitude Plot)
Evaluated along the jω axis (s = jω)