Abstract (eng)
This study was designed to explore the linkages between communication engineering and mathematics. More precisely, the aim was to investigate how information can be transmitted safely. For this reason, the most essential mathematical foundations for communication engineering are introduced.
To begin with, a historical overview including the introduction of the term "communication engineering" and the explanation of Shannon's communication model - the basis of all transmission processes - is presented. Subsequently, the thesis has been divided into two major thematic parts: first, basics from the area of analysis will be explained followed by the basics of coding.
Regarding the area of analysis, the Fourier series as well as the Fourier transformation are analyzed in great detail. However, the main focus lies on the different forms of the Fourier series; especially on the calculation of Fourier coefficients. At this point it shall be noted that this study does not include the convergence of Fourier series due to its limited relevance when it comes to the practice of communication engineering.
In regard to the area of coding, a general introduction is followed by more specific introductions to source coding and channel coding algorithms. The primary focus of this part of the thesis lies on Huffman coding, Lempel-Ziv-Welch coding and Hammingcode as all three remain crucial when it comes to ensuring the secure transmission of information.
During the writing process, both traceability and comprehensibility were regarded as highly important. For this reason, a great number of examples have been included in order to facilitate the comprehension of the underlying theory, especially in the area of coding.