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

Abstract

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 Cramér-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.

Experimentation and Structural Modeling of Stimulus-Evoked Electromyography in Muscles During Electrically-Elicited Fatigue Process

“…Most of the results showed decrease in muscle fiber conduction velocity and reduction in mean/median frequency during the muscle fatigue process [13]. Several studies confirmed that the lengths of stimulated muscle could affect the spectral, temporal, and amplitude features of evoked EMG [13,14,15]. Our previous study indicated that the amplitudes of the evoked EMG of the quadriceps muscle in electrically elicited muscle contractions were significantly different when the knee angle was varied [16].…”

Methods for estimating muscle fibre conduction velocity from surface electromyographic signals

“…For example, spectral compression can be assessed through estimation of the scaling factor between the power spectrum of the signal at the beginning and at the end of the contraction, using other methods than characteristic frequencies (LATERZA et al, 1998). Equivalently, the scaling factor can be computed between the autocorrelation functions of signal segments detected during the contraction, in the case of detection of surface EMG signals elicited by electrical stimulation, the signal itself (the Mwave) scales during time, and thus scale factor estimation can be applied directly to the M-waves (Lo CONTE et al, 1994;LO CONTE and MERLETTI, 1995;MUHAMMAD et al, 2003). The same concepts apply for the analysis of single MU action potentials.…”

“…An example of such a case is the detection of two M-waves from different locations along the muscle fibres. The M-wave detected from the most distant location from the innervation zone will be scaled and delayed with respect to the first one owing to the distribution of CVs of the contributing MUs (MUHAMMAD et al, 2003).…”

Signal detection with noisy reference for passive sensing

“…If the signal to be detected is perfectly known and the noise is stationary with zero-mean and white power spectral density, the optimal detector is the matched filter (MF) which maximizes the output signal-to-noise ratio (SNR) [1]. However, the signal may not be known in many practical applications, such as underwater acoustics [2][3][4][5], seismology [6][7][8][9], neurophysiology [10,11], and passive radar [12][13][14][15][16]. Consider for example passive radar.…”