Abstract: A transversal filter has a transfer function for which a zero point occurs outside a unit circle on z plane and thus the output waveform has a ringing characteristic having a change from negative to positive around a precursor and before a main cursor and is associated and integrated with another transversal filter, thereby forming a waveform shaping decimation filter or a pulse shaping high-pass filter. The waveform decimation filter can eliminate a high frequency noise, changes a high frequency input data to a low frequency output data, and performs a waveform shaping operation. Therefore it cannot require a pulse shaping filter separated from the decimation filter. The pulse shaping high-pass filter includes a pulse shaping filter whose number of the taps is decreased and performs high-pass filter function. A pulse shaping filter whose number of the taps is decreased can be used separately from the high-pass filter.