Pipelining of Lattice IIR Digital Filters

In recent years, rapid advances in VLSI technology have had much impact on modern signal processing. Some of the desirable properties for VLSI realization are regularity, local connection and pipelinability. Lattice digital filters, which have many applications in signal modeling, spectrum estimation, and adaptive filtering, exhibit good finite word-length behavior, but cannot be pipelined to finer levels (such as bit or multi-bit levels) due to the presence of feedback loops. Although lattice filters can be pipelined by the cut-set localization procedure, it should be noted that the maximum sample rate cannot be increased by this technique. In this paper, based upon the properties of the Schur algorithm, a pipelining method in lattice digital filters is introduced, by which the sample rate can be increased at any desired level. By constraining the poles to be located at equal angular and radial spacing, the denominator of the transfer function is forced to be in scattered look-ahead form. It is shown that this transfer function satisfies the pipelining property of lattice filters. Furthermore, based upon state variable description, new methods for scaling and output roundoff noise calculations are introduced; these can be easily applied to lattice IIR digital filters or lattice IIR digital filters connected with other type of filters. The relationship between pipelining stages and the output roundoff noise is analyzed using first and second-order IIR filters. The use of pipelined lattice IIR digital filters in low-power applications is also demonstrated.