Design of interpolative sigma delta modulators via semi-infinite programming

Ho, Charlotte Yuk-Fan and Ling, Bingo Wing-Kuen and Reiss, Joshua D. and Liu, Yan-Qun and Teo, Kok-Lay (2006) Design of interpolative sigma delta modulators via semi-infinite programming. IEEE Transactions on Signal Processing, 54 (10). pp. 4047-4051. ISSN 1053-587x

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Official URL: http://dx.doi.org/10.1109/TSP.2006.880338

Abstract

This paper considers optimized design of
interpolative sigma delta modulators (SDMs). The first
optimization problem is to determine the denominator
coefficients. The objective of the optimization problem is to
minimize the passband energy of the denominator of the loop
filter transfer function (excluding the DC poles) subject to the
continuous constraint of this function defined in the frequency
domain. The second optimization problem is to determine the
numerator coefficients in which the cost function is to minimize
the stopband ripple energy of the loop filter subject to the
stability condition of the noise transfer function (NTF) and signal
transfer function (STF). These two optimization problems are
actually quadratic semi-infinite programming (SIP) problems.
By employing the dual parameterization method, global optimal
solutions that satisfy the corresponding continuous constraints
are guaranteed if the filter length is long enough. The advantages
of this formulation are the guarantee of the stability of the
transfer functions, applicability to design of rational IIR filters
without imposing specific filter structures, and the avoidance of
iterative design of numerator and denominator coefficients. Our
simulation results show that this design yields a significant
improvement in the signal-to-noise ratio (SNR) and have a larger
stability range, compared to the existing designs.

Item Type:Article
Additional Information:This paper considers optimized design of interpolative sigma delta modulators (SDMs). The first optimization problem is to determine the denominator coefficients. The objective of the optimization problem is to minimize the passband energy of the denominator of the loop filter transfer function (excluding the DC poles) subject to the continuous constraint of this function defined in the frequency domain. The second optimization problem is to determine the numerator coefficients in which the cost function is to minimize the stopband ripple energy of the loop filter subject to the stability condition of the noise transfer function (NTF) and signal transfer function (STF). These two optimization problems are actually quadratic semi-infinite programming (SIP) problems. By employing the dual parameterization method, global optimal solutions that satisfy the corresponding continuous constraints are guaranteed if the filter length is long enough. The advantages of this formulation are the guarantee of the stability of the transfer functions, applicability to design of rational IIR filters without imposing specific filter structures, and the avoidance of iterative design of numerator and denominator coefficients. Our simulation results show that this design yields a significant improvement in the signal-to-noise ratio (SNR) and have a larger stability range, compared to the existing designs.
Keywords:Terms—Interpolative sigma delta modulators, noise shaping, stability, semi-infinite programming
Subjects:H Engineering > H600 Electronic and Electrical Engineering
Divisions:College of Science > School of Engineering
ID Code:2711
Deposited By: Rosaline Smith
Deposited On:24 Jun 2010 20:26
Last Modified:13 Mar 2013 08:39

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