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In this paper a concept of time-varying finite impulse response narrow band-stop (notch) filter with improved dynamic behaviour, based on infinite impulse response filter prototype, is proposed. In order to reduce the amplitude of the transient response of the proposed FIR notch filter the pole radius of the IIR filter prototype is temporarily varied in time. Optimization algorithm for finding the parameters for the function of the pole radius is presented. The proposed filters are tested using sinusoid, rectangle, and ECG signals. Computer simulations demonstrate that the proposed time-varying FIR filters outperform traditional time-invariant FIR filters.