Lecture Slides for Signals and Systems (Version: 2016-01-25)

Michael Adams

This document constitutes a detailed set of lecture slides on signals and systems, covering both the continuous-time and discrete-time cases.  Some of the topics considered include: signal properties, elementary signals, system properties, linear-time invariant systems, convolution, Fourier series, Fourier transform, Laplace transform, z transform, complex analysis, and partial fraction expansions.
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Michael Adams
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Published on
Jan 25, 2016
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This book is intended for use in the teaching of graduate and senior undergraduate courses on multiresolution signal and geometry processing in the engineering and related disciplines.  It has been used for several years for teaching purposes in the Department of Electrical and Computer Engineering at the University of Victoria and has been well received by students.

This book provides a comprehensive introduction to multiresolution signal and geometry processing, with a focus on both theory and applications.  The book has two main components, corresponding to multiresolution processing in the contexts of: 1) signal processing and 2) geometry processing.

The signal-processing component of the book studies one-dimensional and multi-dimensional multirate systems, considering multirate structures such as sampling-rate converters, filter banks, and transmultiplexers.  A particularly strong emphasis is placed on filter banks.  Univariate and multivariate wavelet systems are examined, with the biorthogonal and orthonormal cases both being considered.  The relationship between filter banks and wavelet systems is established.  Several applications of filter banks and wavelets in signal processing are covered, including signal coding, image compression, and noise reduction.  For readers interested in image compression, a detailed overview of the JPEG-2000 standard is also provided.  Some other applications of multirate systems are considered, such as transmultiplexers for communication systems (e.g., multicarrier modulation).

The geometry-processing component of the book studies subdivision surfaces and subdivision wavelets.  Some mathematical background relating to geometry processing is provided, including topics such as homogeneous coordinate transformations, manifolds, surface representations, and polygon meshes.  Several subdivision schemes are examined in detail, including the Loop, Kobbelt sqrt(3), and Catmull-Clark methods.  The application of subdivision surfaces in computer graphics is considered.

A detailed introduction to functional analysis is provided, for those who would like a deeper understanding of the mathematics underlying wavelets and filter banks.  For those who are interested in software applications of the material covered in the book, appendices are included that introduce the CGAL and OpenGL libraries.  Also, an appendix on the SPL library (which was developed for use with this book) is included.  Throughout the book, many worked-through examples are provided.  Problem sets are also provided for each major topic covered.
This document constitutes a detailed set of lecture slides on programming using the C++ programming language.  The topics covered are quite broad, including the history of C++, the C++ language itself, the C++ standard library and various other libraries, and software tools, as well as numerous other programming-related topics.  Coverage of C++ is current with the C++14 standard.

Many aspects of the C++ language are covered from introductory to more advanced.  This material includes: language basics (objects, types, values, operators, expressions, control-flow constructs, functions, and namespaces), classes, templates (function, class, alias, and variable templates; template specialization; and variadic templates), lambda expressions, inheritance and run-time polymorphism, exceptions (exception safety, RAII, and smart pointers), rvalue references (move semantics and perfect forwarding), concurrency (sequential consistency, atomic memory operations, data races; threads, mutexes, condition variables, promises and futures, atomics, and fences; happens-before and synchronizes-with relationships; and sequentially-consistent and other memory models).  A number of best practices, tips, and idioms regarding the use of the language are also presented.  Some aspects of the C++ standard library are covered, including: containers, iterators, and algorithms; the std::vector and std::basic_string classes; I/O streams; time measurement; and smart pointers.  Various general programming-related topics are also presented, such as material on: good programming practices, finite-precision arithmetic, software documentation, software build tools (such as CMake and Make), and version control systems (such as Git).
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