Stationary and Non-Stationary Spectral Analysis

News

• There will be a seminar on hearing aids on 8/2 at 13.15 in MH:227. You can find details here.
• The lectures will be held on Tuesdays and Fridays at 13.15-15, starting on Jan. 25. On Friday 8/2, the lecture will be 10.15-12. See below for a detailed schedule.

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 also 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, lecture notes, and research papers.
Time: The lectures will be held on Tuesdays and Fridays at 13.15-13, in MH:362B, starting on Jan. 25. On Friday 8/2, the lecture will be 10.15-12.

Course material

• Errata for Stoica & Moses (edition: 2005, 1997).

Lecture schedule

• Lecture 25/1 - Definitions, AR, MA, ARMA estimation, Line spectra. (AJ)
• Lecture 29/1 - Line spectra. Subspace techniques. (AJ)
• Lecture 1/2 - Non-parametric methods, multi-window techniques. (MS)
• Lecture 5/2 - Data adaptive techniques. (AJ)
• Lecture 8/2 - Spatial spectral analysis. (AJ)
• Lecture 12/2 - Non-stationary signals, spectrogram, Wigner-Ville distibution. (MS)
• Lecture 15/2 - Cohen's class, ambiguity spectrum, Doppler spectrum. (MS)
• Lecture 19/2 - Multi-window techniques for non-stationary signals, reassigned spectrogram, bi-spectra. (MS)
• Lecture 26/2 - Reserve and project discussions. (AJ & MS)
• Lecture TBD - Project presentation. (AJ & MS)

Homework assignments:

The assignments are due at the start of the respective lecture (strict deadline). The problem numbers given in parentheses refers to the 97 edition of the course textbook ant the problems denoted TF are from Maria's lecture notes.

• 5/2: 1.1, 2.1, 2.2, 3.3, C3.20 (C3.18)
• 12/2: C2.21(a,b,c) (C2.19) [only the part under "Variance properties"], C2.22(a,b,c) (C.20), C5.10(a,b) (C5.10), C5.12(a,b) (C5.12)
• 19/2: C4.14 (C4.10), 6.2, C6.17 (C6.14), TF2.1, TF2.2, TF2.3, TFC2.5, TF3.1a)b)
• 26/2: TFC3.4, TF4.1a)b)c)d), TF4.3, TFC4.5, TF6.1, TFC6.4, TF7.2, TFC7.4

You can find the Matlab functions for Maria's notes here.

Suitable further courses

• FMS 110/MAS 222 Non-linear time series analysis.
• FMS 161/MAS 229 Financial statistics.
• FMS 170/MAS 232 Valuation of derivative assets.
• Also, have a look at the available thesis projects.