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Design of optimal and narrow-band Laguerre filters for sigma-delta demodulators

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3 Author(s)
Abeysekera, S.S. ; Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore ; Yao Xue ; Charoensak, C.

Conventional sigma-delta (Σ-Δ) decimation methods are not optimal because the downsampling operation following the noise-shaping filters enables some quantization noise to alias back into the baseband. This paper proposes a novel decimation method that simplifies the implementation of the decimation process. This method makes use of an optimal Laguerre filter as the noise-shaping filter followed by another Laguerre filter that acts as a narrow-band filter. Conventional finite-impulse response (FIR) low-pass filters such as the optimal FIR filter and Sinck filter are commonly used as noise-shaping filters in Σ-Δ demodulators. As an alternative, optimal infinite-impulse response (IIR) filter architecture based on orthonormal Laguerre functions is used in the proposed decimation scheme. An optimal Laguerre IIR filter design methodology is presented via the optimization of a quadratic function subject to a linear and quadratic constraint. An efficient procedure to perform the optimization is introduced. A Laguerre IIR filter can also be used as the narrow-band filter before the decimation process. In this paper, a narrow-band Laguerre filter design methodology is presented via a digital frequency transformation. The narrow-band Laguerre filter can then be efficiently designed using a min-max criterion via a modified Parks-McClellan FIR filter design algorithm.

Published in:

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on  (Volume:50 ,  Issue: 7 )

Date of Publication:

July 2003

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