Abstract: A finite impulse response (FIR) filter is provided for shaping a one bit serial digital data pulse train in a digital data transmission system. The filter comprises (i) a delay element for sequentially receiving binary data bits in the data pulse train at fixed data cycle intervals and outputting simultaneously in parallel a plurality n of data bits representing a most recent history of the past n data bits received by the delay element during the past n data cycle intervals; (ii) a sampling element for sampling the data pulse train at a rate of m samples per bit, and (iii) a memory device having at least (n 30 m) address lines for providing at least 2.sup.(n+m) address locations. The n data bits and m samples provide an input to the address lines, the memory device in response providing a specific precomputed and stored output value for each possible combination of address line inputs.