Linear Systems (Hardcover)

Gordon Blower

ISBN 10: 3031212398 / ISBN 13: 9783031212390

Published by Springer International Publishing AG, Cham, 2023

About this Item

Hardcover. This textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing. The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis. The book mainly covers linear systems with finite-dimensional state spaces. Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB. Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail. The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatars model for multiple antenna transmission. One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system. The final chapter covers modern applications to signal processing, Whittakers sampling theorem for band-limited functions, and Shannons wavelet. Based on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering. The prerequisites are basic linear algebra and complex analysis. This textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783031212390

Bibliographic Details

• Title: Linear Systems (Hardcover)
• Publisher: Springer International Publishing AG, Cham
• Publication Date: 2023
• Language: English
• ISBN 10: 3031212398
• ISBN 13: 9783031212390
• Binding: Hardcover
• Condition: new

About this title

Synopsis

This textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing. The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis.

 

The book mainly covers linear systems with finite-dimensional state spaces. Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB. Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail. The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatar’s model for multiple antenna transmission. One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system. The final chapter covers modern applications to signal processing, Whittaker’s sampling theorem for band-limited functions, and Shannon’s wavelet.

 

Based on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering. The prerequisites are basic linear algebra and complex analysis.

About the Author

Gordon Blower is Professor of Mathematical Analysis at Lancaster University, where he has taught linear systems for several years. His research interests are in random matrix theory and linear systems. In 2021, he organized IWOTA at Lancaster, the main annual international meeting covering applications of operator theory to linear systems and control.