Using SIP techniques to verify the trade-off between SNR and information capacity of a sigma delta modulator

Ling, Wing-Kuen and Ho, Yuk-Fan and Reiss, Joshua (2006) Using SIP techniques to verify the trade-off between SNR and information capacity of a sigma delta modulator. In: 120th Convention of Audio Engineering Society, May 2006, Paris.

Documents
conference_chao_SDM_performance_limit_final_3.pdf
[img]
[Download]
[img] PDF
conference_chao_SDM_performance_limit_final_3.pdf - Whole Document
Restricted to Repository staff only

343Kb

Official URL: http://www.aes.org/e-lib/browse.cfm?elib=13501

Abstract

The Gerzon-Craven noise shaping theorem states that the ideal information capacity of a sigma delta modulator design is achieved if and only if the noise transfer function (NTF) is minimal phase. In this paper, it is found that there is a trade-off between the signal-to-noise ratio (SNR) and the information capacity of the noise shaped channel. In order to verify this result, loop filters satisfying and not satisfying the minimal phase condition of the NTF are designed via semi-infinite programming (SIP) techniques and solved using dual parameterization. Numerical simulation results show that the design with a minimal phase NTF achieves near the ideal information capacity of the noise shaped channel, but the SNR is low. On the other hand, the design with a non-minimal phase NTF achieves a positive value of the information capacity of the noise shaped channel, but the SNR is high. Results are also provided which compare the SIP design technique with Butterworth and Chebyshev structures and ideal theoretical SDMs, and evaluate the performance in terms of SNR and a variety of information theoretic measures which capture noise shaping qualities.

Item Type:Conference or Workshop Item (Paper)
Additional Information:The Gerzon-Craven noise shaping theorem states that the ideal information capacity of a sigma delta modulator design is achieved if and only if the noise transfer function (NTF) is minimal phase. In this paper, it is found that there is a trade-off between the signal-to-noise ratio (SNR) and the information capacity of the noise shaped channel. In order to verify this result, loop filters satisfying and not satisfying the minimal phase condition of the NTF are designed via semi-infinite programming (SIP) techniques and solved using dual parameterization. Numerical simulation results show that the design with a minimal phase NTF achieves near the ideal information capacity of the noise shaped channel, but the SNR is low. On the other hand, the design with a non-minimal phase NTF achieves a positive value of the information capacity of the noise shaped channel, but the SNR is high. Results are also provided which compare the SIP design technique with Butterworth and Chebyshev structures and ideal theoretical SDMs, and evaluate the performance in terms of SNR and a variety of information theoretic measures which capture noise shaping qualities.
Keywords:semi-infinite programming, signal-to-noise ratio, information capacity, sigma delta modulator
Subjects:H Engineering > H310 Dynamics
Divisions:College of Science > School of Engineering
ID Code:3098
Deposited By:INVALID USER
Deposited On:06 Aug 2010 06:07
Last Modified:13 Mar 2013 08:43

Repository Staff Only: item control page