This paper proposes and discusses the noise feedback rounding using an integral‐coefficient digital filter in order to reduce round‐off noise caused by fixed point arithmetic. The following conventions are used; ΓX(z) and ΔX(z) denote the integer and fractional part of a sampled signal X(z), respectively; X(z) is abbreviated as X; N denotes a noise caused by rounding × to Γ (X + R) (R = z‐1 GΔ (X + R)); and the round‐off noise HN under ΔG = 0 at an output is given by HN = K≥, K = ‐H (1 ‐ z‐1 ΓG), N = Δ (1 ‐ z‐1 ΓG)‐1 X where H is the transfer function from a rounding point to the output point. Since N is ordinarily nearly at random, the power of HN can be controlled by determining G for the zeroes of (1 ‐ z‐1 ΓG) to be in the vicinity of the poles of H. In addition, the maximum value Po of the power HN is in the range of 2−2 μ (K) ≤ P0 < μ (K) and therefore μ(K) can be used as an estimator for the worst design value where μ(K) is the maximum value of K(z) K(z‐1) on a unit circle. Both multipliers and combinatorial digital filters described in this paper are simpler in construction and more economical than the ordinary rounding using longer word length or the random rounding.
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