Noise properties of Hilbert transform evaluation

0455229 - FZÚ 2016 RIV GB eng J - Journal Article
Pavlíček, Pavel - Svak, V.
Noise properties of Hilbert transform evaluation.
Measurement Science and Technology. Roč. 26, č. 8 (2015), s. 085207. ISSN 0957-0233. E-ISSN 1361-6501
R&D Projects: GA ČR GA13-12301S
Institutional support: RVO:68378271
Keywords : Hilbert transform * noise * measurement uncertainty * white-light interferometry * fringe-pattern analysis
Subject RIV: BH - Optics, Masers, Lasers
Impact factor: 1.492, year: 2015

The Hilbert transform is a standard method for the calculation of the envelope and phase of a modulated signal in optical measurement methods. Usually, the intensity of light is converted into an electric signal at a detector. Therefore the actual spatially or temporally sampled signal is always affected by noise. Because the noise values of individual samples are independent, the noise can be considered as white. If the envelope and phase are calculated from the noised signal, they will also be affected by the noise. We calculate the variance and spectral density of both the envelope noise and the phase noise. We determine which parameters influence the variance and spectral density of both the envelope noise and the phase noise. Finally, we determine the influence of the noise on the measurement uncertainty in white-light interferometry and fringe-pattern analysis.

Permanent Link: http://hdl.handle.net/11104/0255879