Proposes a 'quantum Hilbert transform' via state-dependent phase shifts in the Fourier basis, but the rule does not reproduce the classical Hilbert transform and is not a fixed quantum operation.
The Basic Discrete Hilbert Transform with an Information Hiding Application
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abstract
This paper presents several experimental findings related to the basic discrete Hilbert transform. The errors in the use of a finite set of the transform values have been tabulated for the more commonly used functions. The error can be quite small and, for example, it is of the order of 10^{-17} for the chirp signal. The use of the discrete Hilbert transform in hiding information is presented.
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Quantum Hilbert Transform
Proposes a 'quantum Hilbert transform' via state-dependent phase shifts in the Fourier basis, but the rule does not reproduce the classical Hilbert transform and is not a fixed quantum operation.