# Scaling Properties of Superoscillations and the Extension to Periodic Signals

@article{Tang2015ScalingPO, title={Scaling Properties of Superoscillations and the Extension to Periodic Signals}, author={Eugene Tang and Lovneesh Garg and Achim Kempf}, journal={arXiv: Mathematical Physics}, year={2015} }

Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more pronounced the desired superoscillatory behavior is to be, the more difficult it becomes to produce, or even only calculate, such highly fine-tuned wave forms in practice. Here, we investigate how this sensitivity to preparation errors scales for a method for… Expand

#### 6 Citations

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A function f is said to possess superoscillations if, in a finite region, f oscillates faster than the shortest wavelength that occurs in the Fourier transform of f. I will discuss four aspects of… Expand

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Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many… Expand

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Superoscillating functions, i.e., functions that locally oscillate at a rate faster than their highest Fourier component, are of interest for applications from fundamental physics to engineering.… Expand

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By reviewing the mathematical methods for constructing superoscillations, including their considerations and capabilities, this review lays out the options for anyone wanting to construct a device that uses superoscills, and highlights areas for future theoretical development to enable the scientific and technological boundaries to be pushed even further in real-world applications. Expand

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A new numerically stable method for constructing superoscillatory wave forms in an arbitrary number of dimensions that allows the construction of superoscilling square-integrable functions that match any desired smooth behavior in their superoscilled region to arbitrary accuracy. Expand

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