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

• Published in: IEEE transactions on circuits and systems. 2, Analog and digital signal processing Vol. 50; no. 7; pp. 368 - 375
• Main Authors: Abeysekera, S.S., Yao Xue, Charoensak, C.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Delta-sigma modulation; Demodulation; Design methodology; Finite impulse response filter; IIR filters; Low pass filters; Narrowband; Noise; Noise shaping; Quantization; Studies
• ISSN: 1057-7130; 1558-125X
• DOI: 10.1109/TCSII.2003.813588

Conventional sigma-delta (/spl Sigma/-/spl Delta/) 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 Sinc/sup k/ filter are commonly used as noise-shaping filters in /spl Sigma/-/spl Delta/ 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.