A design of the scale parameter of wavelet transform for the estimation of transition time in PWL systems

This paper proposes a method to determine an appropriate scale parameter of wavelet transform for the estimation of transition time of the PieceWise Linear (PWL) systems by using wavelet analysis. Precision of the estimation of transition time depends on the scale parameter of wavelet transform under noisy environment. Effect of the noise on the estimation of transition time is shown under the assumption of Gaussian random noise in a numerical example. Appropriate range of the scale parameter of wavelet transform is determined by using quantified the effect of the noise and effectiveness of the method is illustrated by numerical experiments.