# Geometric interpretation of signals: background

### David G. Messerschmitt

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2006-91

June 27, 2006

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-91.pdf

This tutorial report describes how signals can be modeled as vectors in a Hilbert space, and highlights some of the geometric properties and interpretations that result. Two specific examples are highlighted: the space of square-integrable continuous-time signals, and the space of random variables with finite second moments. Some useful theorems from Hilbert space theory, such as the projection theorem, are shown to have useful application to optimization problems encountered in signal processing.

BibTeX citation:

@techreport{Messerschmitt:EECS-2006-91, Author = {Messerschmitt, David G.}, Title = {Geometric interpretation of signals: background}, Institution = {EECS Department, University of California, Berkeley}, Year = {2006}, Month = {Jun}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-91.html}, Number = {UCB/EECS-2006-91}, Abstract = {This tutorial report describes how signals can be modeled as vectors in a Hilbert space, and highlights some of the geometric properties and interpretations that result. Two specific examples are highlighted: the space of square-integrable continuous-time signals, and the space of random variables with finite second moments. Some useful theorems from Hilbert space theory, such as the projection theorem, are shown to have useful application to optimization problems encountered in signal processing.} }

EndNote citation:

%0 Report %A Messerschmitt, David G. %T Geometric interpretation of signals: background %I EECS Department, University of California, Berkeley %D 2006 %8 June 27 %@ UCB/EECS-2006-91 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-91.html %F Messerschmitt:EECS-2006-91