Hilbert Space Methods in Signal Processing

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.

• The only book to cover signal processing on the unit sphere for applications in engineering and applied sciences such as geodesy and astronomy
• Includes historical anecdotes on important and influential people who contributed to the development of the theory
• Features over 100 worked problems, carefully chosen to make additional points, to motivate the reader and to deepen and broaden their understanding
• Explains the theory of reproducing kernel Hilbert spaces from a novel angle