Reduction of the Gibbs phenomenon in the special case of non-harmonic time base distortions

This paper presents a sine wave fitting procedure for characterizing measurements of a harmonic signal in the presence of additive noise and an unknown time base distortion. In general the reconstructed time base distortion of the existing solutions (Verspecht, 1994; Schoukens et al., 1997) suffers from the Gibbs phenomenon (ringing) at the borders of the data record. Ignoring data samples at the borders is unacceptable for very short data records where measuring a sample is (very) expensive and/or (very) time consuming. This paper presents a solution that suppresses the Gibbs phenomenon in the estimated time base distortion without ignoring data samples at the borders. The theory is illustrated on simulations and on real measurements of the vessel density of a mangrove tree from Kenya (Rhizophora mucronata).