Eytan Katzav, Moshe Schwartz
Super-oscillating signals are band limited signals that oscillate in some region faster their largest Fourier component. While such signals have many scientific and technological applications, their actual use is hampered by the fact that an overwhelming proportion of the energy goes into that part of the signal, which is not super-oscillating. In the present article we consider the problem of optimization of such signals. The optimization that we describe here is that of the super-oscillation yield, the ratio of the energy in the super-oscillations to the total energy of the signal, given the range and frequency of the super-oscillations. The constrained optimization leads to a generalized eigenvalue problem, which is solved numerically. It is noteworthy that it is possible, to still increase the super-oscillation yield at the cost of slightly deforming the oscillatory part of the signal, while keeping the average frequency. We show, how this can be done gradually, which enables a trade-off between the distortion and the yield.
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http://arxiv.org/abs/1209.6572
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