## A Short Introduction to Gabor Analysis

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