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. For example, one may apply linear transformations with the aim that the information can be read off more easily from the new representation of the signal. Such transformations are used for many diverse tasks such as analysis and diagnostics, compression and coding, transmission and reconstruction.
KeywordsFilter Bank Riesz Basis Dual Frame Gabor Frame Short Time Fourier Transform
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