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227-0689 System Identification

The course uses the Piazza web platform for class discussions. All course material (including exercises and exams) and announcements will posted on the Piazza class site.

General Information

Term: Autumn semester
Lecturer: Prof. Roy Smith
Lectures: Wednesdays 10.15-12.00 in HG E 1.2
Exercise sessions: Wednesdays 12.15-13.00 in ETZ D 61


Familiarity with the following concepts is assumed:

  • Laplace and Fourier transforms;
  • Z-transform;
  • Differential and difference equations;
  • State-space representations;
  • Basic stochastic variable concepts.

Course Material

Lecture number Lecture content Last revised
1 Introduction 04.10.17
2 Frequency domain methods: spectra, system responses, and estimated transfer functions 27.09.17
3 ETFE and spectral estimation 04.10.17
4 Averaging and smoothing 11.10.17
5 Time-domain windows and input signals 18.10.17
6 Residual spectra, coherency, aperiodicity, offsets and drifts 25.10.17
7 Frequency domain subspace ID 01.11.17
8 Closed-loop identification 07.11.17
9 Time-domain parametrisations, correlation, persistency of excitation, ARX and equation error models 15.11.17
10 Prediction error methods 22.11.17
11 Parameter estimation statistics, instrumental variable methods 29.11.17
12 ARX and IV examples, validation 06.12.17
13 Time-domain subspace identification 12.12.17

Unfortunately there are several commonly used, but different, formulae for equivalent concepts. This can lead to confusion and these notation notes discuss some of the pitfalls for beginning readers of the literature.

The lectures are be video recorded and posted on the ETH Videoportal.

Matlab functions

The following functions are provided to save you the time and trouble of coding them yourself. They are not optimized and so will not work well for very large data sets.


Related papers

Material from the following papers are discussed in the lectures. The papers are here so that you can read the details.

Primary reference

  • "System Identification; Theory for the User", Lennart Ljung, Prentice Hall (2nd Ed), 1999.

Secondary references

There are many texts that cover the required background in digital signals. The following are good but be aware that the notation varies a lot between texts so read carefully.

  • Fourier Transform, Digital signals processing (basics): "Signals & Systems," A.V. Oppenheim, A.S. Willsky with S.H. Nawab (2nd Ed.) Prentice-Hall, 1983.
  • More advanced digital signal processing: "Digital Signal Processing," A.V. Oppenheim & R.W. Schafer, Prentice-Hall, 1975.
  • Spectral analysis: "Introduction to Spectral Analysis," P. Stoica & R. Moses, Prentice-Hall, 1997.