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Nonlinear Signal Processing: Structure vs. Behavior


R. Pearson

Graz University of Technology, Graz, Austria, Institute of Communications and Wave Propagation.

Many classical signal processing problems are closely related to linear discrete-time dynamic models, with two important examples being linear filter design and parametric spectral estimation. There are, however, problems where nonlinear structures are required, as in the design of data cleaning filters to remove outliers (e.g., impulsive noise) from corrupted data sequences or the design of modulator/ demodulator pairs for chaotic communication schemes. An important difference between linear and nonlinear dynamic models is that structural and behavioral descriptions are essentially equivalent in the linear case, but this equivalence breaks down in a number of surprising ways in the nonlinear case. The focus of this lecture is on three potentially useful relaxations of linear behavior (specifically, weakenings of the principle of superposition) and their structural consequences, emphasizing their utility in signal processing applications. Well-known examples from each of these classes are noted and various partial structural characterizations and closure properties are used to obtain some interesting new structures.


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(05)Plenary/Invited/Honorary Lecture

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