Note on nonparametric spectral analysis of wideband spectrum with missing data via sample-and-hold interpolation and deconvolution

Abstract

In [1] a procedure for bias-free estimation of the autocorrelation function is introduced for equidistantly sampled data with randomly occurring samples being invalid. The method incorporates sample-and-hold interpolation of the missing data points. The occurring dynamic error of the primary estimate of the correlation function is treated by a deconvolution procedure with two parameters c0 and c1 with c0+2c1=1, which are the on-diagonal and the aside-diagonal parameters of a specific correction matrix (at all lag times except zero). The parameters c0 and c1 were obtained as a function of the probability α of a sample to be valid by numerical simulation. However, explicit expressions for the parameters c0(α)=1−2α+2α2 and c1(α)=1α−1α2 can be derived, which might improve the usability of the deconvolution procedure in [1].