A description of the mathematical basis of signal processing, and many areas of application.

1. Introduction D. Rockmore and D. Healy; 2. Hyperbolic geometry, Nehari's theorem, electric circuits, and analog signal processing J. Allen and D. Healy; 3. Engineering applications of the motion-group Fourier transform G. Chirikjian and Y. Wang; 4. Fast x-ray and beamlet transforms for three-dimensional data D. Donoho and O. Levi; 5. Fourier analysis and phylogenetic trees S. Evans; 6. Diffuse tomography as a source of challenging nonlinear inverse problems for a general class of networks A. Grunbaum; 7. An invitation to matrix-valued spherical functions A. Grunbaum, I. Pacharoni and J. Tirao; 8. Image registration for MRI P. Kostelec and S. Periaswamy; 9. The mathematics of JPEG 2000 Jin Li; 10. Integrated sensing and processing for statistical pattern recognition C. Priebe, D. Marchette and D. Healy; 11. Sampling of functions and sections for compact groups D. Maslen; 12. The Cooley-Tukey FFT and group theory D. Maslen and D. Rockmore; 13. Mathematical challenges for optical communications U. Osterberg; 14. The generalized spike process, sparsity and statistical independence N. Saito.