Derivation of the Optimum Tapered Weight for the Burg Algorithm with Decimation and Its Application for Measurement of Thickness of a Thin Multi-layer Film

Abstract

The optimum tapered Burg (OTB) algorithm is based on minimization of the average variance of the estimated frequency of a sinusoid. The decimation technique has also been used to resolve clearly sinusoids of closely spaced frequencies. This paper newly derives the optimum tapered weight for the Burg algorithm with decimation and shows that the variance of the estimated frequency becomes even smaller than that of the OTB algorithm. The decimation technique with this optimum tapered weight is applied to measure sub-micron thickness of multi layer film and its effectiveness is shown.