1. Introduction -- 2. Fourier series and Fourier transforms -- 3. Remote sensing -- 4. Finite-parameter models -- 5. Transmission and remote sensing -- 6. The Fourier transform and convolution filtering -- 7. Infinite sequences and discrete filters -- 8. Convolution and the vector DFT -- 9. Plane-wave propagation -- 10. The phase problem -- 11. Transmission tomography -- 12. Random sequences -- 13. Nonlinear methods -- 14. Discrete entropy maximization -- 15. Analysis and synthesis -- 16. Wavelets -- 17. The BLUE and the Kalman filter -- 18. Signal detection and estimation -- 19. Inner products -- 20. Wiener filtering -- 21. Matrix theory -- 22. Compressed sensing -- 23. Probability -- 24. Using the wave equation -- 25. Reconstruction in Hilbert space -- 26. Some theory of Fourier analysis -- 27. Reverberation and echo cancellation.