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The effective bandwidth of a signal can significantly vary in time. To improve sampling efficiency, it would be desirable, therefore, to be able to sample at a correspondingly time-varying rate while maintaining the ability to stably reconstruct the signal from its samples. Fourier theory is too rigid for this purpose but functional analytic tools have allowed a suitable generalization of Shannon...
Shannon sampling theory, which is in ubiquitous use in communication engineering and signal processing, shows that in order to record all information contained in a Omega-bandlimited continuous signal it suffices to record samples of the signal's amplitude at discrete points in time, namely at the so-called Nyquist rate of 2Omega samples per second. It is clear, however, that for realistic signals...
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