Motivation: Although Fourier Analysis can look back on a history of almost 200 years now and is thus a mature field, the last decades have seen an enormous development of practical and theoretical Fourier analysis, which so far has not found its way into the standard course, given to mathematicians or engineers. In fact, the way how Fourier Analysis, or on the applied side often ``Signal Analysis and Systems Theory'' is taught in engineering schools is using quite different methods, making it hard, to move between the theoretical side and the more practical side of the field. Given the fact that modern technology (mobile communication, data compression, digital imaging, medical or geophysical data processing) is making heavy use of different variants of Fourier analysis many of our students and colleagues are not aware of the new perspectives and teach the subject in a traditional way. Well presented YOUTUBE presentations at prestigious universities are no exception.