Hilbert transform of a narrowband periodically non-stationary random signal (PNRS) is considered. The relations for the covariance components of PNRS and its Hilbert transform are obtained. The dependencies of the covariance properties of Hilbert transform on covariance damping coefficients of modulating processes are analyzed on the basis of the simulated realizations.
The calculation of the coefficients of linear system transfer function with the lumped constant parameters which corresponds to the preset frequency response is present.
Calculation of the transfer function on a given frequency response is the optimization problem. Direct solution has multiextremal nonlinear optimization.
Hilbert transform is applied to calculate the minimum-phase phase response. Therefore, the optimization problem of calculating the coefficients of the transfer function has complex goal function with some restrictions.
In this paper theoretical fundamentals of white light interferometry and mathematical model of interferogramm were analyzed. The method of topography reconstruction from phase of white-light interferogramm based on amplitude demodulation using Hilbert transform was developed. The verification of introduced algorithm on tilted and sphere surface is presented and the main sources of reconstruction errors were analyzed.