NOISE-REDUCTION IN RECURSIVE DIGITAL-FILTERS USING HIGH-ORDER ERROR FEEDBACK

The problem of solving the optimal (minimum-noise) error feedback coefficients for recursive digital filters is addressed in the general high-order case. It is shown that when minimum noise variance at the filter output is required, the optimization problem leads to a set of familiar Wiener-Hopf or Yule-Walker equations, demonstrating that the optimal error feedback can be interpreted as a special case of Wiener filtering. As an alternative to the optimal solution, the formulas for suboptimal error feedback with symmetric or antisymmetric coefficients are derived. In addition, the design of error feedback using power-of-two coefficients is discussed. These schemes are often more suitable for practical implementation than the optimal error feedback and in many cases almost as good roundoff noise performance is achieved. The efficiency of high-order error feedback is examined by test implementations of the set of standard filters. It is concluded that the error feedback is a very powerful and versatile method to cut down the quantization noise in any classical IIR filter implemented as a cascade of second-order direct form sections. Second-order error feedback is sufficient for most cascade implementations, whereas the new high-order schemes are attractive for use with high-order direct form sections.