Design of an Efficient IIR Filter for SIGMA – DELTA Modulation

The problem of designing an IIR digital filter to minimize the output filtered quantization noise power in sigma-delta modulation is attempted. Employing the 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 an even power polynomial with unknown coefficients and its denominator is chosen as the linear phase polynomial which is strictly Hurwitz. The filter coefficients are optimized with respect to a comparable SincN filter. Finally, the digital representation of the filter is extracted from its analog counterpart. It is shown that the design achieves a considerable saving in the filter size while keeping a comparable characteristic to the much larger FIR comb filter.