Aim
The aim of the course is to give basic understanding of the topics digital signal processing and digital communications. Their relation is illustrated especially through examples based on the modulation scheme OFDM.

Knowledge and understanding
For a passing grade the student must

• be able to identify and formulate problems within the area of digital signal processing and digital communications.

• be able to classify the level of difficulty of problems related to the his/her own level of knowledge.

• be able to modell and structure basic digital filters and communication schemes.

Skills and abilities
For a passing grade the student must

• be able to apply his/her mathematical knowledge in aplications based on digital signal processing and digital communications.

• be able to show ability to handle new concepts, methods and results.

Judgement and approach
For a passing grade the student must

• be able to show insight concerning possibilities and limitations of digital signal processing and digital communications.

Contents
Introduction: The course gives an overview of the related areas digital signal processing and digital communication. Their relation is especially shown with examples from the modulation technique Orthogonal Frequency Division Multiplexing (OFDM), used ig for example ADSL and WLAN.

Digital Signal Processing: Deterministic modells for signals and signal processing systems are described, with examples from communication techniques. The mathematical tools Discrete Fourier Transform and Z-transform are defined. Important concepts like frequency function and transfer function is used and different types of basic filters are discussed. The structural chain for systems based on digital signal processing is described and illustrates how an analog signal is sampled and A/D converted, and recreated with with D/A convertion. Different methods for processing are desribed and basic filters classified. Aliasing is considered both in time and frequency domain.

Digital Communications: A digital communication system can be viewed as the conversion of the chain for digital signal processing. Digitally stored data is translated to digital signals according to a modulation scheme. These are transformed to a analog media by D/A conversion. On the receiver side the signal is A/D converted for the system to be able to decode the transmitted data. Different modulation schemes, like PSK, PAM and QAM, are introduced. The transmission with background noise is modelled with stochastic methods, and an optimal receiver is discussed.

Literature
Mitra, K: Digital Signal Processing, A Computer-Based Approach. McGraw-Hill, 3rdedition.
Introduction to Digital Communications, Lecture notes