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Stationary and Non-stationary spectral analysis


  • The course material is now available via the below link. Additional files will be added as the course progresses. 

Course contents

The course provides an overview of different modern techniques in statistical spectral analysis, for both stationary and non-stationary signals and processes, with material that ranges between statistics and signal processing. The purpose of the course is to deepen and widen the knowledge for such methods, as there is a large need for more advanced techniques in many application areas, e.g., communication and medicine. The course will contain material on basic definitions and an overview of classical non-parametric methods. Furthermore, more statistically robust techniques that have become more common during recent years will be covered, such as subspace-based parametric techniques and non-parametric data-adaptive and multi-taper methods. The course also covers non-uniform sampling, non-circular processes, and spatial spectral analysis, topics that find applications in an ever-growing number of fields. Time-frequency analysis is a modern tool for investigation of non-stationary signals and processes. The research in this area has expanded during the last 20 years, making this is a common tool for analysis. The course will cover both classical and modern time-frequency approaches. Many applications will be presented and discussed during the course and the participants will work with real data.

Higher education credits: 7,5 Level: A

Language of instruction: This course may be offered in English (if non-Swedish speaking students are attending).

Recommended prerequisites: Basic courses in probability and statistics, stochastic processes and time series analysis

Assessment: Written and oral project presentation and hand-ins.


  • Stoica & Moses, 'Spectral analysis of signals', Prentice-Hall, 2005. 
  • Maria Sandsten, 'Time-Frequency Analysis of Time-Varying Signals and Non-Stationary Processes: An Introduction', 2018.
  • The course material and the relevant literature can be found here.

Preliminary schedule

  • Lecture 1, Definitions, AR, MA, ARMA estimation, Line spectra. (AJ)
  • Lecture 2, Line spectra. Subspace techniques. (AJ)
  • Lecture 3, The spectrogram and the Wigner distribution. (MS)
  • Lecture 4, The ambiguity function and ambiguity kernels. (MS)
  • Lecture 5, Data adaptive techniques. (AJ)
  • Lecture 6, Spatial spectral analysis. (AJ)
  • Lecture 7, Time-frequency distributions and multitapers. (MS)
  • Lecture 8, Optimal resolution and stochastic time-frequency analysis. (MS)
  • Project presentation, TBD. (AJ & MS) 

The detailed schedule can be found here.

Course start

First Lecture:
Monday, January 15, 2018, at 10.15, in MH:309A

Reading periods:



Andreas Jakobsson, 046-222 45 20

Maria Sandsten, 046-222 49 53

Course secretary:

Maria Lövgren, 046-222 45 77