Course Syllabus for

# Stationary and Non-stationary Spectral Analysis StationĂ¤r och icke-stationĂ¤r spektralanalys

## FMSN35F, 7.5 credits

Valid from: Spring 2014
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-02-27

## General Information

Division: Mathematical Statistics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMSN35
Teaching language: English

## Aim

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.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• 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.

Competences and Skills

For a passing grade the doctoral student must

• 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.

## Course Contents

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.

## Course Literature

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

## Instruction Details

Types of instruction: Lectures, exercises, project

## Examination Details

Examination formats: Written report, written assignments, seminars given by participants