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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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 Sciences > Faculty of Science > Lincoln School of Engineering
Depositing User:	Rosaline Smith
Date Deposited:	24 Jun 2010 20:26
Last Modified:	13 Mar 2013 08:39
URI:	http://eprints.lincoln.ac.uk/id/eprint/2711

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