Estimating from outputs of oversampled delta-sigma modulation

Oversampling a delta-sigma-modulated sequence, one can compute unbiased sample estimates of averages of consecutive input elements for a wide variety of inputs. We prove that these estimates are most e cient in their class (that is, variances of sample means are minimum in the class of random binary sequences gn, n = 1; : : : ; N , such that the expected values of gn are equal to the values of the corresponding inputs of delta-sigma modulation) and consistent. Delta-sigma modulation may also be described as one-dimensional error di usion (a technique for digital halftoning). However, delta-sigmamodulation is not a practical digital halftoning algorithm, because human vision averages small luminance deviations in two dimensions. We pose an open problem that invites the reader to extend our approach to the two-dimensional case for the purpose of development of a practical digital halftoning algorithm. IEEE EDICS number: SP 3.8.2 Correspondence should be sent to: Dmitri A. Gusev Indiana University Computer Science Department Lindley Hall Bloomington, IN 47405-4101 e-mail: [email protected] phone: (812) 855-9109