The safety system has restraint device (RD) and an acceleration sensor (DS) determining the vehicle acceleration the output of which is converted in an A/D converter (AD) into a digital signal. A Wavelet transformation processor (WF) transforms the digital signal into a Wavelet coefficient using a Wavelet function which is prepared on the basis of a function of a time located displaced master Wavelet function, scaled as a function of a scale parameter and of a shift parameter which indicates a time location. A speed change calculator (VC) establishes a first condition when the transformed Wavelet coefficient exceeds a specific value and the output signal of the A/D converter is integrated for a specific time to derive a speed change. An actuator (OM) establishes a second condition when the change in speed exceeds a specific value and operates the safety device when both conditions are fulfilled.
