One important problem of signal processing in measurement systems is designing a filter that possesses a linear-phase response and, at the same time, has a short transient state. This paper presents the methodology of varying, in the time parameters, a low-pass Bessel filter and a filter of a constant component. In the proposed filters, significant shortening of the transient state is achieved at the cost of a slight increase in oscillations. This paper also addresses the problems that are connected with continuous running of the filters with varying parameters. The presented approach allows better preservation of the edge shape, as compared with traditional filtering techniques. Typical filtering results are presented, which are obtained by simulations of selected structures of filters with varying parameters.