FMSN35F

Aktiv

Stationary and Non-stationary Spectral Analysis

7.5

Gemensam kurs, avancerad nivå och forskarnivå

7152 (Centre of Mathematical Sciences / Mathematical Statistics)

 -02-27

FN1/Anders Gustafsson

English

Varannan vårtermin

This course is aimed at those who want to broaden and deepen their knowledge in statistical signal processing and expand their toolkit with more advanced techniques. The course lies on the border between statistics and signal processing and builds on the classical non-parametric methods that are well-known and taught in courses like Stationary stochastic processes or Optimal signal processing. Since these methods are not always sufficient we need more advanced techniques in many application areas, e.g. communication or medicine. Hence, the course covers more statistically robust methods that have become increasingly used in recent years, e.g. time-frequency analysis, which is a modern method for analysis of non-stationary signals and processes. The research in this area has expanded during the last 20 years, making this a commonly used tool. Many applications will be presented in the course and the participants will work with real world data.

Basic definitions. Extended studies of AR (auto regressive), MA (moving average) och ARMA-processes. Linespectra and parametric estimation methods. Noise-space based techniques. Non-parametric spectral estimators, data-adaptive techniques and multitaper methods. Non-uniform sampling. Orientation of circular and non-circular processes. Spatial spectral analysis. Non-stationary processes. Spectrogram. Wigner-Ville distribution. Cohen class. Ambiguity spectrum. Multitaper techniques for non-stationary signals. Orientation about bispectrum.

Be able to interpret and understand parametric and non-parametric spectral estimation methods.
Be able to interpret and understand spatial spectral analysis and classical estimation techniques of directions.
Be able to interpret and understand time-frequency analysis and classical estimation techniques of non-stationary spectra.

Be able to estimate classical parametric and non-parametric spectral estimates.
Be able to estimate spectra of non-uniformly sampled sequences.
Be able to use classical time-frequency methods for estimation.

Föreläsningar

övningar

Projekt

Skriftlig rapport

Inlämningsuppgifter

Seminarieföredrag av deltagarna

Underkänd, godkänd

Sandsten, M.: Lecture notes: Time-frequency analysis. 2011.

FMSN35F

 -02-27

FN1/Anders Gustafsson