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Superoscillations with Optimal Numerical Stability
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DOI：10.1109/LSP.2014.2339731.png)
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Abstract
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A bandlimited signal can oscillate at a rate faster than its bandlimit. This phenomenon, called superoscillation, has applications e.g. in superresolution and superdirectivity. The synthesis of superoscillations is a numerically difficult problem. We introduce time translation as a design parameter and give an explicit closed formula for the condition number of the matrix of the problem, as a function of. This enables us to determine the best possible condition number, which is several orders of magnitude better than otherwise achievable.
Keywords:
Algorithms
condition number
Hilbert space
interpolation
matrices
nonuniform sampling
numerical stability
sampling methods
signal design
superoscillations
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