A digital filter includes a pair of serially connected second order sections (200 and 260), each of which includes delay elements arranged to store the number of bits contained in two complete input words. Each filter section also includes simple logic (220, 230, 270 and 280) comprising adder circuits and inverters but no multipliers. The logic combines outputs from the delay element with the filter input to form an intermediate signal which is applied to the input of the delay element. The intermediate signal is also combined with yet other outputs from the delay element to form the filter output. To eliminate clocking complexity within the filter, the logic is not preset or cleared between each input word. Instead, the word length is intentionally increased, and the sign bit of each intermediate word is intentionally repeated as the word is processed in the filter, the extra bits acting as an inter-word buffer and serving to protect against spurious overflow and limit cycle oscillations.