Title :
On the role of differential geometry in signal processing
Author :
Manton, Jonathan H.
Author_Institution :
Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Vic., Australia
Abstract :
Traditionally, the majority of non-linear signal processing problems were tackled either by appropriate linearisations or by some ad hoc technique. By contrast, linear signal processing problems are routinely solved systematically by astute application of results from linear algebra. This paper shows by example how differential geometry provides the necessary tools and mindset for systematically solving certain non-linear problems commonly encountered in signal processing.
Keywords :
differential geometry; differentiation; signal processing; Grassmann manifold; Jacobian matrix; Stiefel manifold; differential calculus; differential geometry; nonlinear signal processing; Calculus; Geometry; Jacobian matrices; Linear algebra; Machinery; Manifolds; Signal analysis; Signal processing; Vectors; Visualization;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP '05). IEEE International Conference on
Print_ISBN :
0-7803-8874-7
DOI :
10.1109/ICASSP.2005.1416480
