An improved family of exponentially accurate sigma-delta quantization schemes

EA-modulation is an A/D-conversion method which represents a bandlimited signal by sequences of ±1 whose local averages approximate the function values. The best bounds for the decay rate of the ℓ_∞-error arising from such quantization schemes have been given by Güntürk. ¹ He constructs an infinite family of schemes which lead to an algorithm that establishes exponential error decay with decay rate 0.077. In this paper we improve his construction introducing an additional symmetry, which is suggested by numerical experiments. To show that the modified schemes are still stable, we use the asymptotics of the Γ-function. This leads to a bound of 0.088 for the error decay rate.