Book: Modern Signal Processing (Mathematical Sciences Research Institute Publications)
Publisher: Cambridge University Press
The mathematical basis of signal processing and its many areas of application is the subject of this book. Based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute, the volume emphasizes current challenges, new techniques adapted to new technologies, and certain recent advances in algorithms and theory.
Underlying many of the current mathematical opportunities in digital signal processing are unsolved analog signal processing problems. For instance, digital signals for communication or sensing must map into an analog format for transmission through a physical layer. In this layer we meet a canonical example of analog signal processing: the electrical engineer’s impedance matching problem. Impedance matching is the design of analog signal processing circuits to minimize loss and distortion as the signal moves from its source into the propagation medium. This paper works the matching problem from theory to sampled data, exploiting links between H1 theory, hyperbolic geometry, and matching circuits. We apply J. W. Helton’s significant extensions of operator theory, convex analysis, and optimization theory to demonstrate new approaches and research opportunities in this fundamental problem.