2015/01/08 by Or Ordentlich, Ordentlich, Or, Uri Erez +1
Computer Science · Engineering · Mathematics · #Analog and Mixed-Signal Circuit Design #Digital Filter Design and Implementation #FOS: Computer and information sciences #Information Theory (cs.IT) #Numerical Methods and Algorithms #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1501.01829
openalex publication_date 2015/01/08 · arxiv created 2015/06/09 · arxiv updated 2015/06/10 · openalex created_date 2022/09/25 · openalex updated_date 2026/07/28
Sampling above the Nyquist rate is at the heart of sigma-delta modulation, where the increase in sampling rate is translated to a reduction in the overall (mean-squared-error) reconstruction distortion. This is attained by using a feedback filter at the encoder, in conjunction with a low-pass filter at the decoder. The goal of this work is to characterize the optimal trade-off between the per-sample quantization rate and the resulting mean-squared-error distortion, under various restrictions on the feedback filter. To this end, we establish a duality relation between the performance of sigma-delta modulation, and that of differential pulse-code modulation when applied to (discrete-time) band-limited inputs. As the optimal trade-off for the latter scheme is fully understood, the full characterization for sigma-delta modulation, as well as the optimal feedback filters, immediately follow.