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