APPENDIX Mathematical Complements

Important mathematical concepts are reviewed without proof. Sections A.1 through A.5 we present results of real and complex analysis, including properties of Hilbert spaces, bases, and linear operators [59]. Random vectors and Dirac distributions are covered in the last two sections.

A.1 FUNCTIONS AND INTEGRATION

Analog signals are modeled by measurable functions. We first give the main theorems of Lebesgue integration. A function f is said to be integrable if image. The space of integrable functions is written as . Two functions f1 and f2 are equal in if

This means that f1(t) and f2(t) can differ only on a set ...

Get A Wavelet Tour of Signal Processing, 3rd Edition now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.