This volume provides an overview of the wide range of mathematical topics in signal processing. The focus is on alternative algebras for signal processing, particularly multilinear and geometric algebra and Gröbner bases. Other topics include array processing and digital communications, wavelets, nonlinear signal processing, Padé approximation, convex optimization, and generalized eigenvalue decomposition. Blending theory and practice, the volume will appeal to a wide range of engineers and mathematicians.