Digital signal processing has become more and more an integral part of observational seismology. While it offers unprecedented power in extracting information from seismic signals, it comes at the price of having to learn a variety of new skills. Dealing with digital seismic data requires at least a basic understanding of digital signal processing. Taking the calculation of true ground motion as the guiding problem, this course covers the basic theory of linear systems, the design and analysis of simple digital filters, the effect of sampling and A/D conversion and an introduction to spectral analysis of digital signals. It contains a number of examples and exercises that can be reproduced using the PITSA software package (Scherbaum and Johnson 1993) or similar programs.