## 1 Introduction  
Measuring devices usually operate in noised environments. The source of the noise can vary, depending on the measured physical quantity [1; 2]. In the electrical engineering area, one of the most-often measured quantities is the voltage value, derived from sensors (e.g., the weight transformed to the voltage output of tensometers). Unfortunately, voltage measurements can be easily noised by other electrical equipment around the sensors. The noise source is often an integral part of the measured object itself [3]. For example, the measurement of DC motor speed is conducted by magnetic encoders which are usually placed at the end of the motor shaft. Significant noise can be also generated by equipment placed within a close vicinity of the sensor [4]. For example, power lines can affect the measurements of biomedical signals [5].  
One of the most important problems in filtering measurement signals is the transient response of the filters used. The duration of the transient depends mainly on the order and the selectivity of the filter. Long transients may cause very significant problems, particularly when short time-signals are processed, or when the initial stage of a filtered signal is of great importance. In such situations, a useful signal can be considerably distorted due to the presence of the transient of the filter, or the signal can be entirely lost in the transient state.  
In this paper, a concept for a digital parameter-varying infinite impulse response (IIR) lowpass filter with a transient response of short duration is presented. The proposed digital filter is based on an analog oscillatory system, which is subjected to the discretization process. The improvement of the dynamic behavior attained by the proposed filter structure is based on temporary changes in the value of dynamical parameters of the analog filter prototype [6; 7].  
The methodology proposed for the variation of filter parameters has been used, with some modifications, in a few applications. For example, in [8], a time-varying analog filter was used to eliminate the oscillatory response exhibited by the load cells used in weighing applications. Another time-varying filter was used, in [9], to reduce the time employed in the acquisition of evoked potentials generated through auditory stimuli. Moreover, in [10], the parameter-varying strategy was used to reduce the transient response of filters with a compensated group delay response. As the concept was proved to be very useful, the methodology was only tested with exponential decay functions as the time-varying base, dictated by the implementation reliability and repeatability demands with analog passive elements. This paper is a further extension of our research into the time-varying coefficients concept in the digital signal processing area, where more complex time-varying base functions are easily achieved. We propose to use a known analog oscillatory system as the basis for the digital time-varying filtering structure. We also present a new method for obtaining the sets of coefficients that improve the transient response of the considered system.  
The paper is organized as follows: In Section 2, the considered oscillatory system and its discrete counterpart are presented. The idea of the IIR filter with time-varying parameters is presented in Section 3. In Section 4, the strategy used to optimize the variability of filter parameters, in order to reduce the transient response, is presented. Section 5 presents and discusses the real-life implementation and measurement of the rotary speed of a motor with the proposed parameter-varying filtering structure. Finally, some concluding remarks are given in Section 6.