Chair of
Multimedia Communications and Signal Processing
Prof. Dr.-Ing. André Kaup

Analysis of numerical methods

Field of activity: Multidimensional Signals and Systems Theory
Research topic: Multidimensional Signals and Systems
Staff: Prof. Dr.-Ing. habil. Rudolf Rabenstein

Processing discrete-time, discrete-space signals requires numerical methods to obtain a multidimensional signal for one time step from the previous time steps. These numerical methods can be derived from various sources.

A first approach is to extend well-known concepts from one-dimensional signals to multiple dimensions. This way multidimensional FIR and IIR filters have been defined and state-space models for multidimensional systems have been introduced.

Another classical source is the numerical solution of partial differential equations. Examples for numerical methods from this field are the digital wave guide (DWG) method for sound synthesis and the finite difference time domain (FDTD) method for the simulation of acoustic wave propagation.

Furthermore also control theory has developed methods which explicitely consider the
boundedness of the space variables. The so-called repetitive processes extend the classical
multidimensional state-space processes by additional terms which represent finite spatial extension
and boundary conditions.

Research in this field aims at unifying these different concepts on the basis of multidimensional signals and systems. Especially stability investigations for multidimensional systems are extended to iterative methods and to repetitive processes.

 

Solution of an implicit finite difference scheme with Gauss-Seidel iteration
represented as a discrete multidimensional system with three coordinates: space, time, iteration
number

Publications

2013-37
CRIS
M. Friedrich
   [link]   [bib]

Reduction of Dominant Interference to Patient Speech Communication at Magnetic Resonance Tomography Systems
Verlag Dr. Hut, München, 2013