Signal Theory

Unified Signal Theory is an indispensible textbook dealing with the theory of deterministic signals; a topic of fundamental interest to graduates and senior undergraduates in the areas of information engineering (telecommunications, control, systems theory and electronics), astronomy, oceanography, earth science, biology and medicine.

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.

Nonlinear signal and image processing methods are fast emerging as an alternative to established linear methods for meeting the challenges of increasingly sophisticated applications.

Adaptive Signal Models: Theory, Algorithms and Audio Applications presents methods for deriving mathematical models of natural signals. The introduction covers the fundamentals of analysis-synthesis systems and signal representations. Some of the topics in the introduction include perfect and near-perfect reconstruction, the distinction between parametric and nonparametric methods, the role of compaction in signal modeling, basic and overcomplete signal expansions, and time-frequency resolution issues. These topics arise throughout the book as do a number of other topics such as filter banks and multiresolution.