Abstract-The use of the delta operator in the realizations of digital filters has recently gained interest due to its good finite-word-length performance under fast sampling. We studied efficient direct form structures, and show that only some of them can be used in delta configurations, while others are evidently unstable. In this paper, we focus on the roundoff noise analysis. Of all the direct-form structures, the direct form II transposed (DFIIt) delta structure has the lowest quantization noise level at its output. This structure outperforms both the conventional direct-form (delay) structures, as well as the state-space structures for narrow-band low-pass filters with respect to output roundoff noise. Excellent roundoff noise performance is achieved at the cost of only a minor additional implementation complexity when compared with the corresponding delay realization. Complexity of a signal processor implementation of the DFIIt delta structure, which was found to be the most suitable delta structure for signal processors, is compared with those of the direct form and state-space delay structures. In addition, some hardware implementation aspects are discussed, including the minimization of the internal word length.Index Terms-Delta operator, direct-form structures, roundoff noise.

Delta operator realizations of IIR filters have recently received a lot of interest due to their good finite-wordlength properties.Here we present a detailed analysis of the computationally efficient transposed direct form I1 delta structure, which is also known to have excellent roundoff noise performance under fast sampling. Focus is on the roundoff noise minimization in fixedpoint implementations. The free A parameter in the delta operator is optimized with respect to the output roundoff noise within the scaling constraints. Moreover, required internal wordlength to obtain prespecified noise performance is derived.

No abstract

The roundoff noise and coefficient sensitivity performance of the delta operator realized recursive digital filters have been shown to be good under fast sampling. Recently it has been found out that in fixed point delta operator implementations limit cycles may occur. We have proposed a small but important modification into the delta operator which enables us to eliminate zero-input limit cycles completely if magnitude truncation quantization is used. In this paper, we study in detail the scaling and roundoff noise in the modified delta operator direct form structure when magnitude truncation is used.

No abstract