Associate Professor Parastoo Sadeghi – Book

Research School of Engineering
College of Engineering and Computer Science
Australian National University

Hilbert Space Methods in Signal Processing

[1] R. A. Kennedy and P. Sadeghi, "Hilbert Space Methods in Signal Processing", Cambridge University Press, Cambridge, UK, March 2013.
Abstract BibTeX
Google-Scholar: [link]
title = {Hilbert Space Methods in Signal Processing},
author = {Kennedy, R. A. and Sadeghi, P.},
publisher = {Cambridge University Press},
address = {Cambridge, UK},
month = {March},
year = {2013}}

Official Book Description


This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite’, which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formalised. Having addressed fundamental topics in Hilbert spaces, the authors then go on to cover the theory of bounded, compact and integral operators at an advanced but accessible level. Finally, the theory is put into action, considering signal processing on the unit sphere, as well as reproducing kernel Hilbert spaces. The text is interspersed with historical comments about central figures in the development of the theory, which helps bring the subject to life.

Links Relevant to the Book


page 26, missing norm in triangle inequality


The formula should read:

\[ \|f+g\| \le \|f\|+\|g\|,\quad \forall f,g\in\mathcal{H}.\hspace{20mm}(2.4) \]

page 337, two corrections in Remark 10.6

These should read, respectively, "\(\text{as }n \rightarrow \infty\)" and "\(\text{convergence}\)"

page 350, typo

This should read \(\text{"associate"}\)