## 1 Introduction  
Estimation, detection and filtering of narrowband signals in the presence of unwanted noise represent some of the important applications of signal processing techniques. In most of these applications it is often desired to suppress narrowband signals while leaving the broad band energy without changes. This can be achieved by passing the signals through a band reject filter whose notches are centered on the narrowband signals. Typical application areas include for example biomedical engineering and communications [1; 2]. Removing powerline interferences from ECG, EEG, and EMG recordings [3], filtering of humming GSM mobile telephone noise [4], and estimation of power system frequency [5] are specific examples of using notch filters. The design procedure of notch filters is usually a difficult task, particularly when the signals on a very narrow frequency band must be suppressed and those in the immediate neighborhood should be maintained without distortions. From the measurement point of view one of the most important problems of the signal processing path is the transient response of filters. The duration of the transient state depends mainly on the filter order and the filter selectivity [6]. Long-lasting transients cause huge problems, particularly when short-time signals are filtered or when the initial phase of a processed signal is of great importance [7; 8; 9]. In such cases a useful signal can be considerably distorted due to the presence of the filter transient response or the signal can be entirely lost in the transient. In many measurement-signal processing systems it is required to use notch filters which possess at the same time a very selective magnitude response and a short duration of the transient response. In the design of filters, however, the selective magnitude response and the transient response of short duration are design specifications which are contradictory to each other and, therefore, are very difficult to tune in a simultaneous way.  
The trade off between the duration of the transient response and the selectivity of notch filters has been examined in a few works. In [10; 11] the authors introduce non-zero initial conditions to the output of notch filters. As a result, the transient response of these filters is considerably suppressed. On the other hand, in [12], the notch filters with a time-varying quality factor and time-varying pole radius are proposed. The proposed time-varying notch filters are characterized by exponential variability of their parameters. By introducing time-varying parameters to the filter structure the authors attain a significant reduction of the duration of the transient response of notch filters. The results they obtained clearly show that the proposed methods are effective at filtering ECG signals.  
In this paper, the second order digital infinite impulse response notch filter with reduced transient response is proposed. In order to suppress the transient response of the considered infinite impulse response (IIR) notch filter its pole radius is temporarily varied in time using the Bezier parametric curve. Computer simulations verifying the effectiveness of the proposed strategy clearly show that the Bezier curve is definitely more effective in reducing the duration of the transient response if compared to previously used exponential functions [12; 13]. The rest of this paper is organized as follows: in Section 2, digital IIR notch filters are discussed in more detail. The idea of the IIR notch filter with a time-varying pole radius is presented in Section 3. In Section 4, examples of using the proposed pole-radius-varying notch filter to filtering ECG signals distorted by powerline interference are provided. Finally, some concluding remarks are given in Section 5.