Reduction of the Gibbs phenomenon applied on nonharmonic time base distortions

A sine wave fitting procedure for characterizing measurements of a periodic signal in the presence of additive noise and an unknown time base distortion is presented. If the time base distortion is modeled by a Fourier series, it suffers from the Gibbs phenomenon (ringing) at the borders of the data record. Usually, this is solved by ignoring data samples at the borders. The latter 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 ringing in the estimated time base distortion without ignoring data samples at the borders. The theory is illustrated on simulations and on real vessel density in the wood of a mangrove tree from Kenya (Rhizophora mucronata).