Restoration of the signal and its spectral characteristics with an irregular set of measurements

An extension of the algorithm for singular value decomposition (SVD)-based restoration of the signal is suggested that makes it possible to gain information on the dynamics of spectral lines (response of the medium) recorded in a single series of irregular measurements of the signal’s integral characteristics with the help of a sliding window. The size and displacement of the window fluctuate in time. SVD-based restoration is accomplished both directly from irregular measurement data and after interpolation of the data to the nodes of a regular grid. An algorithm of signal restoration that is based on spline interpolation is also proposed. When combined with SVD-based restoration, this algorithm allows almost complete elimination of spurious frequencies. In the case of integral measurements using an irregular-size window with its center displaced, the signal restoration quality and determination of the spectral line dynamics are shown to be no worse than in the case of fluctuation-free measurements. Analysis is performed both for a model signal and for the real response considered earlier in the physical experiment.