On a variational approach to the extraction of quadratures from broadband reflectometry signals

Abstract

A variational method is employed to retrieve the phase from broadband reflectometry signals. The method yields the so-called in-phase and quadrature components of a signal (the signal quadratures in short), by stipulating that these should have the smallest possible amount of functional variation, whereby the signal carrier frequency is also recovered as a by-product. The variational approach is based on the reasonable assumption that, for given data, the quadratures are expected to be as slow as possible, as they contain the slow modulations of amplitude and phase, while rapid variations are accounted for by the carrier frequency. The advantages and shortcomings of the variational method are discussed, and a pertinent comparison with the analytic signal—recently proposed as a means to extract the phase from broadband reflectometry signals—is also carried out. The application of the variational method to the reflectometry problem is shown to yield results that are similar to those obtained via the analytic signal. The difference is not significant, especially if detailed measurements are not required, but only averaged ones.