The interesting properties of a class of expanding systems are discussed. The operation of the considered systems can be described as follows: the input signal is processed by a linear dynamic converter in subsequent time intervals, each of them is equal to Ti. Processing starts at the moments n · Ti, always after zeroing of converter initial conditions. For smooth input signals and a given transfer function of the converter one can suitably choose Ti and the gain coefficient in order to realize the postulated linear operations on input signals, which is quite different comparing it to the operation realized by the converter. The errors of postulated operations are mainly caused by non-smooth components of the input signal. The principles for choice of system parameters and rules for system optimization are presented in the paper. The referring examples are attached too.