Estimation of slight speed gaps between signals via the scale transform

In this paper, we consider signals measured on mechanical systems whose speed may be slightly different from one recording to the other, the speed value being not accurately known. In order to match experimental signals together or with their theoretical model, we propose a method for estimating the slight speed gaps between them. First, we specify the conditions under which a speed gap can be approximated by a time-scaling. Thus, we can write: x2(t)=x1(a(t−t0)), and we show that the scale factor a, linked to the relative speed gap between x1 and x2, can be estimated via a logarithmic resampling of both autocorrelation functions or both spectrums of signals. A development of this idea leads to use a particular case of the Mellin transform: the scale transform, whose phase is known to be affected by time-scalings. We so propose a method for estimating the speed gap between two signals using the discrete scale transforms of the autocorrelation functions. Advantage is to avoid the logarithmic resampling scheme. Performance of the method are discussed on simulations and on real signals: acceleration signals measured on a chairlift when passing over a compression pylon and gear transmission error signals.