Stationary and Non-Stationary Spectral Analysis


  • The course is offered next time in the spring of 2018.

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.

The course consist of lectures, hand-ins, and computer exercises/projects.

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, stationary stochastic processes, as well as time series analysis.
Assessment: Written and oral project presentation and hand-ins.

Literature: Stoica & Moses, Spectral analysis of signals, Prentice-Hall, 2005. It is available electronically here, or in a high-resolution chapter per chapter version here. The old version of the book (Stoica & Moses, Introduction to Spectral Analysis, Prentice-Hall, 1997) also includes everything needed for the course.

Maria Sandsten, Time-Frequency Analysis of Time-Varying Signals and Non-Stationary Processes: An Introduction, 2016 Time-Frequency Analysis,

Time: See below for lecture rooms and dates. A detailed schedule for the course can be found here.

Course material

  • The compendium by Maria Sandsten are available here.
  • The textbook by Stoica & Moses is available electronically here, or in a high-resolution chapter per chapter version here.
  • Errata for Stoica & Moses (edition: 2005, 1997).
  • Matlab functions for Stoica & Moses can be found here.
  • The list of projects can be found here.

Lecture schedule

  • Lecture 1, 18/1, 10-12, MH:227 -Definitions, AR, MA, ARMA estimation, Line spectra. (AJ)
  • Lecture 2, 22/1, 13-15, MH:333 - Line spectra. Subspace techniques. (AJ)
  • Lecture 3, 25/1, 10-12, MH:333 - Non-parametric methods, multi-window techniques. (MS)
  • Lecture 4, 29/1, 13-15, MH:333 - Data adaptive techniques. (AJ)
  • Lecture 5, 1/2, 10-12, MH:227 - Spatial spectral analysis. (AJ)
  • Lecture 6, 5/2, 13-15, MH:333 - Spectrogram, Wigner-Ville distribution, Cross-terms, Ambiguity function. (MS)
  • Project presentation, TBD. (AJ & MS)

Homework assignments:

To be specified.

Suitable further courses



Last modified: Oct 28, 2016

Course Start

First meeting:
18/1, 10-12, MH:227

Reading periods:


Andreas Jakobsson Maria Sandsten Assistants:


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Centre for Mathematical Sciences, Box 118, SE-22100, Lund. Telefon: +46 46-222 00 00 (vx)