A pseudojoint estimation of time delay and scale factor for M-wave analysis

A pseudojoint estimation of time scale and time delay between an unknown deterministic transient type signal and a reference signal is proposed. The method is based on the separation between the estimations of the two dependent parameters. The time autocorrelation function (TACF) preserves the time scale and is invariant with respect to the time delay between the signals. The time scale factor can, thus, be estimated independently from time delay using the TACFs of the two signals. After estimating the time scale factor, the signal can be scaled by the estimated amount. The time delay is then estimated without bias due to the time scale factor. To obtain high resolution joint estimates, the time scale factor is estimated in the scale domain from the scale transforms of the TACFs of the two signals. The proposed method has low computational cost. Moreover, the results on synthetic signals show good performance of the method with respect to the Cramer-Rao lower bound and the joint maximum likelihood estimation. A possible application of the technique to the analysis of electromyogram (EMG) signals detected during electrically elicited contractions is also presented. In a few representative cases, it is shown that the time scale estimate reveals myoelectric manifestations of muscle fatigue and is less affected by M-wave truncation than spectral EMG attributes.