Array Beamforming with Linear Difference Equations

This book explores the relationship between differential beamforming and linear difference equations, offering new insights and methods for beamforming, noise reduction, and applications in speech enhancement through various mathematical perspectives.

Array Beamforming with Linear Difference Equations explores the connection between differential beamforming techniques and linear difference equations, offering fresh insights into beamforming theory and methods. The authors begin by outlining the key challenges and methodologies associated with beamforming, along with commonly used performance metrics that help in evaluating and optimizing beamformers.

The book delves into the intricacies of first-order, second-order, and higher-order linear difference equations, demonstrating how these concepts can be applied to formulate and address various beamforming problems. The discussion includes both fixed and adaptive beamforming methods, highlighting how these approaches can be utilized to enhance performance in real-world applications.

In addition to theoretical insights, the authors apply the principles of linear difference equations to the realm of speech enhancement, deriving several noise reduction filters such as the maximum signal-to-noise ratio (SNR) filter, the Wiener filter, and the minimum variance distortionless response (MVDR) filter. The text also examines the relationship between difference equations and differential beamforming through the lens of spectral graph theory, providing a comprehensive understanding of the subject. Overall, this book serves as a valuable resource for researchers and practitioners looking to deepen their knowledge of beamforming techniques and their mathematical foundations.