In order to analyze and describe complicated phenomena, mathematicians, engineers and physicists like to represent them as a superposition of simple, well-understood objects. A significant part of research has gone into the development of methods to find such representations. These methods have become important in many areas of our scientific and technological activity. They are used for instance in telecommunications, medical imaging, geophysics, and engineering. An important aspect of many of these representations is the chance to extract relevant information from a signal or the underlying process, which is actually present but hidden in its complex representation.
Over many years the Fourier transform was the main tools in applied mathematics and signal processing for these purposes. But due to the large diversity of problems with which science is confronted on a regular basis, it is clear that there does not exist a single universal method which is well adapted to all those problem simultaneously.
Here is an overview on several streams of development, leading up to what is nowadays called Gabor analysis. For more details see [FS98].
The NuHAG Gabor Server