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Transfer Functions, Poles & Zeros, Stability via the ROC
Inside this lesson
- Define the transfer function H(s) = Y(s)/X(s) for an LTI system under zero initial conditions and relate it to the frequency response H(jω)
- Identify the poles and zeros of a rational transfer function and interpret each pole as a natural mode e^(pt)u(t)
- State and apply the BIBO stability criterion for causal LTI systems: all poles must lie strictly in the left half-plane
- Construct and interpret a pole-zero plot on the s-plane
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Educational content covering topics typical of a first- and second-year electrical engineering curriculum. Not a substitute for accredited coursework, and not suitable for real antenna, transmission-line, or signal-processing system design without review by a licensed professional engineer.