Each module contains 3 ECTS. You choose a total of 10 modules/30 ECTS in the following module categories:

- 12-15 ECTS in technical scientific modules (TSM)

TSM modules teach profile-specific specialist skills and supplement the decentralised specialisation modules. - 9-12 ECTS in fundamental theoretical principles modules (FTP)

FTP modules deal with theoretical fundamentals such as higher mathematics, physics, information theory, chemistry, etc. They will teach more detailed, abstract scientific knowledge and help you to bridge the gap between abstraction and application that is so important for innovation. - 6-9 ECTS in context modules (CM)

CM modules will impart additional skills in areas such as technology management, business administration, communication, project management, patent law, contract law, etc.

In the module description (download pdf) you find the entire language information per module divided into the following categories:

- instruction
- documentation
- examination

The goal of this module is to introduce the students to the powerful world of statistical digital signal processing. While at the bachelor level digital signal processing is most often taught with deterministic signals, in the real world most interesting signals are stochastic in nature. Hence in more advanced applications, such as prediction or noise removal, the theories presented in this module are essential.

The basic digital signal processing, linear algebra and probability theory necessary to understand the module are brushed-up at the beginning. Then stochastic processes are introduced which allows the proper formulation of the optimal filtering and spectral estimation problem later on. After an in-depth treatment of the optimal filtering and estimation problem, adaptive filters are introduced which are a popular choice for many advanced statistical digital signal processing problems.

### Prerequisites

Understanding of the following concepts at the Bachelor of Science level

• Calculus

• Linear algebra

• Probability/Statistics

• Digital signal processing

### Learning Objectives

• The student becomes familiar with stochastic signals and systems

• The student understands and can apply the different methods for signal modeling

• The student has an in-depth understanding of Wiener filtering and knows how a discrete Kalman filter can be used to solve a stochastic filtering problem

• The student understands and can apply the different methods for spectrum estimation

• The student knows the most common adaptive filters and is able to select the proper one for the application at hand

### Contents of Module

The module starts with a review of basic digital signal processing, linear algebra and probability theory. It then introduces some concepts about stochastic processes, which are necessary to understand the following applications of statistical signal processing. Then the module discusses several different ways of signal modeling which can be used for parametric methods later on. Then one of the core topics is presented, which is the optimal linear mean square error estimation of a signal which is corrupted by additive noise. The module then presents a chapter about the very important topic of spectral estimation and finally concludes with the application of the learned theory for designing adaptive filters.

The available 14 weeks are organized as follows:

• 2 weeks: Background (review of digital signal processing and linear algebra)

• 3 weeks. Discrete-time random processes (including a review of probability)

• 2 weeks: Signal modeling

• 3 weeks: Wiener filtering (including the discrete Kalman Filter)

• 2 weeks: Spectrum estimation

• 2 weeks: Adaptive filtering

### Teaching and Learning Methods

• A three hour session each week for 14 weeks

• The first hour is a homework review session where the homework is discussed. The homework is “paper and pencil” homework and small Matlab programming assignments

• The next two hours are lecture hours, where new theory is introduced

### Literature

“Statistical Digital Signal Processing and Modeling” by Monson H. Hayes

Download full module description

Back