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VLSI Digital Signal Processing Systems: Design and Implementation by Keshab K. Parhi

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10.4    PIPELINING IN HIGHER-ORDER IIR DIGITAL FILTERS

This section presents approaches for pipelining higher-order recursive digital filter topologies using clustered and scattered look-ahead techniques. (For 1st- order IIR filters, these two look-ahead approaches reduce to the same form.) With clustered look-ahead, pipelined realizations require a linear complexity in the number of loop pipeline stages and are not always guaranteed to be stable. We illustrate the use of scattered look-ahead approach to derive stable pipelined filters. Then the decomposition technique is revisited in this section for higher-order IIR filters and is used to obtain area-efficient implementations for higher-order filters. In addition to the clustered and the scattered lookahead techniques, constrained filter design techniques that achieve pipelining without pole-zero cancellation are discussed.

Let the transfer function of an N-th order direct-form recursive filter be described by

image

Equivalently, the output sample y(n) can be described in terms of the input

image

Fig. 10.7   (a) Pole zero location of a 12-stage pipelined 1st-order recursive filter. (b) Decomposition of the zeros of the pipelined filter for a 2 × 3 × 2 decomposition.

sample u(n), and the past input and output samples, and is given by

Again, ...

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