Transfer Function Analysis and Perfect Tracking

Created on May 30, 2025

2025   ·   control-systems   signal-processing   ·   research

Transfer functions describe how a linear time-invariant (LTI) system transforms inputs into outputs. Transfer functions provide a compact, frequency-domain view of system dynamics, making it easy to analyze stability, and fundamental performance limits.

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Outline:

  • Why transfer functions are such a powerful abstraction.
  • How zeros, poles, and factorizations shape system behavior.
  • What “perfect tracking” means in both the time and frequency domains.
  • Why non-minimum-phase systems fundamentally block perfect tracking.
  • Visualizations and worked examples.


If you found this useful, please cite this as:

Buchanan, E. Kelly (May 2025). Transfer Function Analysis and Perfect Tracking. https://ekellbuch.github.io.

or as a BibTeX entry:

@article{buchanan2025transfer-function-analysis-and-perfect-tracking,
  title   = {Transfer Function Analysis and Perfect Tracking},
  author  = {Buchanan, E. Kelly},
  year    = {2025},
  month   = {May},
  url     = {https://ekellbuch.github.io/blog/2025/transfer-function-analysis/}
}