Spectral analysis is introduced by B. Hofmann-Wellenhof and H. Moritz from the Institute of Theoretical Geodesy, Technical University of Graz. The text discusses linear equation systems and the concept of convolution. It explains that convolution involves multiplication followed by summation, and later, integration. The goal of spectral analysis is to eliminate the summation or integration part of convolutions. The text then considers a diagonal matrix, which simplifies the linear equation system. For a diagonal matrix, the system becomes straightforward, with each equation involving only one variable. This is shown through an example with a 3x3 diagonal matrix, where each equation is simply a scalar multiple of the corresponding variable. The text highlights that this simplification makes the analysis of such systems much easier. The discussion is part of a broader context of spectral analysis, which aims to simplify and understand complex systems through the use of matrices and transformations. The text provides a foundation for understanding how spectral analysis can be applied to various problems, particularly in geodesy and related fields. The content is structured to introduce key concepts and their applications, setting the stage for further exploration into the topic.Spectral analysis is introduced by B. Hofmann-Wellenhof and H. Moritz from the Institute of Theoretical Geodesy, Technical University of Graz. The text discusses linear equation systems and the concept of convolution. It explains that convolution involves multiplication followed by summation, and later, integration. The goal of spectral analysis is to eliminate the summation or integration part of convolutions. The text then considers a diagonal matrix, which simplifies the linear equation system. For a diagonal matrix, the system becomes straightforward, with each equation involving only one variable. This is shown through an example with a 3x3 diagonal matrix, where each equation is simply a scalar multiple of the corresponding variable. The text highlights that this simplification makes the analysis of such systems much easier. The discussion is part of a broader context of spectral analysis, which aims to simplify and understand complex systems through the use of matrices and transformations. The text provides a foundation for understanding how spectral analysis can be applied to various problems, particularly in geodesy and related fields. The content is structured to introduce key concepts and their applications, setting the stage for further exploration into the topic.