Design of Narrow Band Decimation Filter for Sigma Delta Modulator

This paper is concerned with investigating the problem of designing an IIR digital filter to minimize the filtered quantization noise power in Sigma-Delta modulation. Employing bilinear transformation, the filter is designed first in the analog frequency domain. Its transfer function is assumed to be a rational function with its numerator being a power polynomial with unknown coefficients and its denominator is chosen as a linear phase polynomial which is strictly Hurwitz. The filter coefficients are optimized to minimize the output high frequency quantized noise power. Finally, the digital representation of the filter is extracted from its analog counterpart. It is shown that the design achieves a good saving in the filter size while maintaining a comparable characteristic to the much larger FIR comb filter. Further, it is shown that with proper choice of parameters, the filter is quite stable to variations in tap coefficient values due to the finite word length. To gain confidence in the design, a simulation is conducted on several cases with excellent agreement between the theoretical and the simulated results.