The Windowed Fourier Transform
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Current research is to a large extent motivated by industrial applications of mathematical analysis and signal processing. Seismic exploration, the analysis and synthesis of sound, medical imaging, and the digital telephone are a few of the applications that come to mind. In all cases, one wishes to extract from the signal the pertinent information as discrete numerical values. This set of digital information must be rich enough to characterize the signal, but it should be no larger than necessary for the task at hand. If, for example, it is a question of speech and the digital telephone, one wants enough numerical information at the receiver to reconstruct a recognizable voice, but economy dictates the need to minimize the amount of information that must be transmitted.