Transform methods stands at the center of signal processing, which encompasses everything from satellite communications to medical imaging, from acoustics to spectroscopy. Fourier analysis, in the guise of X-ray crystallography, was essential to Watson and Crick's discovery of the double helix, and it continues to be important for the study of protein and viral structures. The Fourier and allied transforms are fundamental tools, both theoretically and computationally, in the solution of partial differential equations. As such, it's at the heart of mathematical physics, from Fourier's analytic theory of heat to the most modern treatments of quantum mechanics. Any kind of wave phenomenon, be it seismic, tidal, or electromagnetic, is a candidate for Fourier analysis. Many statistical processes, such as the removal of "noise" from data and computing correlations, are also based on with Fourier and allied transforms.  More »