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This paper presents a practical approach for, cancelling a periodic interference from signal measurements. In the method the waveform of the interference is continuously estimated and subtracted from the measurement. The rejection properties are made independent of small variations in the fundamental frequency of the interference by fixing the sampling rate to be an exact multiple of it. Special attention is paid to the line frequency interference rejection problem where the notch at each harmonic is required to be very narrow although the sampling frequency is high if compared with the lowest notch frequency. Implementations using finite impulse response (FIR) and infinite impulse response (IIR) discretetime filters are discussed. The proposed filters are shown to be easier to implement in wideband multiple notch applications than conventional and adaptive digital filters. A digital line frequency interference eliminator requiring only two multipliers has been constructed using an IIR filter. All of its 128 notches are 1-Hz wide and over 70-dB deep at 50 Hz and at its harmonics. The sampling frequency is 25.6 kHz and the available signal bandwidth is 6.4 kHz. The compensation of the low-frequency behavior of the digital IIR filter has been accomplished by combining appropriately analog filters with the digital part. The resulting frequency response with essentially linear phase characteristics starts from zero frequency. Through multiplexing the filter can also be used as a two- or four-channel system.