Stationary and Non-stationary Spectral Analysis
Stationär och icke-stationär spektralanalys

FMSN35F, 7.5 högskolepoäng

Gäller från och med: Spring 2014
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2014-02-27

Allmänna uppgifter

Avdelning: Mathematical Statistics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMSN35
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

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.

Kurslitteratur

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

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, övningar, projekt

Kursens examination

Examinationsformer: Skriftlig rapport, inlämningsuppgifter, seminarieföredrag av deltagarna
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:

• Andreas Jakobsson <andreas.jakobsson@matstat.lu.se>
• Maria Sandsten <maria.sandsten@matstat.lu.se>