Additive and multiplicative abrupt jump detection using the continuous wavelet transform

This paper addresses the problem of additive and multiplicative abrupt jump detection. Two detection algorithms based on the continuous wavelet transform are studied. Additive and multiplicative jumps are compared in the time-scale plane. Considering non-zero mean signals, we show that the same wavelet based algorithms can be used for the detection of additive and multiplicative jumps. However, an analysis of the variance in the time-scale plane allows us to distinguish these two kinds of jump.