Delta operator realizations of direct-form IIR filters

摘要

The use of the delta operator in the realizations of digitalnfilters has recently gained interest due to its good finite-word-lengthnperformance under fast sampling. We studied efficient direct formnstructures, and show that only some of them can be used in deltanconfigurations, while others are evidently unstable. In this paper, wenfocus on the roundoff noise analysis. Of all the direct-form structures,nthe direct form II transposed (DFIIt) delta structure has the lowestnquantization noise level at its output. This structure outperforms bothnthe conventional direct-form (delay) structures, as well as thenstate-space structures for narrow-band low-pass filters with respect tonoutput roundoff noise. Excellent roundoff noise performance is achievednat the cost of only a minor additional implementation complexity whenncompared with the corresponding delay realization. Complexity of ansignal processor implementation of the DFIIt delta structure, which wasnfound to be the most suitable delta structure for signal processors, isncompared with those of the direct form and state-space delay structures.nIn addition, some hardware implementation aspects are discussed,nincluding the minimization of the internal word length