# Geometric interpretation of signals: applications

### David G. Messerschmitt

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2006-92

June 27, 2006

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-92.pdf

This tutorial report describes some important applications of the geometric modeling of signals to signal processing. The idea of stationary signals (deterministic and stochastic) is related to geometric properties. Linear prediction is shown to be an application of the Hilbert space projection theorem. Sampling is shown to be the solution to a minimum-distance optimzation problem. Finally, the lattice filter and its important properties are derived from first principles using a geometric approach.

BibTeX citation:

@techreport{Messerschmitt:EECS-2006-92, Author = {Messerschmitt, David G.}, Title = {Geometric interpretation of signals: applications}, Institution = {EECS Department, University of California, Berkeley}, Year = {2006}, Month = {Jun}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-92.html}, Number = {UCB/EECS-2006-92}, Abstract = {This tutorial report describes some important applications of the geometric modeling of signals to signal processing. The idea of stationary signals (deterministic and stochastic) is related to geometric properties. Linear prediction is shown to be an application of the Hilbert space projection theorem. Sampling is shown to be the solution to a minimum-distance optimzation problem. Finally, the lattice filter and its important properties are derived from first principles using a geometric approach.} }

EndNote citation:

%0 Report %A Messerschmitt, David G. %T Geometric interpretation of signals: applications %I EECS Department, University of California, Berkeley %D 2006 %8 June 27 %@ UCB/EECS-2006-92 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-92.html %F Messerschmitt:EECS-2006-92