TY - JOUR
T1 - Performance analysis and optimal filter design for sigma-delta modulation via duality with DPCM
AU - Ordentlich, Or
AU - Erez, Uri
N1 - Funding Information: Manuscript received June 9, 2015; revised January 22, 2018; accepted October 30, 2018. Date of publication November 16, 2018; date of current version January 18, 2019. O. Ordentlich was supported by the ISF under Grant 1791/17. U. Erez was supported by the ISF under Grant 1956/17. This paper was presented in part at the 2015 International Symposium on Information Theory [1]. Publisher Copyright: © 2018 IEEE.
PY - 2019/2
Y1 - 2019/2
N2 - 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 paper 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 the performance 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 follows.
AB - 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 paper 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 the performance 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 follows.
KW - Quantization
KW - analog-to-digital conversion
KW - differential pulse-code modulation
KW - sigma-delta modulation
UR - http://www.scopus.com/inward/record.url?scp=85056735087&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/TIT.2018.2881750
DO - https://doi.org/10.1109/TIT.2018.2881750
M3 - Article
SN - 0018-9448
VL - 65
SP - 1153
EP - 1164
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 2
M1 - 8537788
ER -