using digital signal processing in a modem attached to a digital line , the modem sample rate for both transmit and receive signals is interpolated or decimated to the time slot rate of a digital channel connected to the modem by filters which are operated by a unified interpolation / decimation filter controller as a function of a modulo counter . for example , a modem signal is developed as if it were to be supplied to a codec . however , instead of being supplied to the codec , the signal is filtered using a low pass finite impulse response digital filter . the resulting filtered signal is sampled at the time slot rate and supplied in companded form as an output to the time slots of the digital line . prior to operating the filter , the ratio of the time slot rate to the sample rate is determined . the ratio is expressed in a form that is a ratio of the smallest possible integers . the numerator of the resulting ratio is designated p and the denominator is designated i . the coordination between the development of the modem signal sample and the filter operation is under the control of a modulo counter that has a modulus of p .