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260                                                Chapter 6 DSP Algorithms






























                               Figure 6.54 Functional pipeline



        6.8.4 Pipeline Interleaving
        Pipeline interleaving can be used, for example, when several signals are to be pro-
        cessed by the same algorithm [13, 14, 18, 19]. We demonstrate pipeline interleav-
        ing by means of an example. Consider a second-order section in direct form with
        the transfer function




            Now, if each delay element is replaced by two delay elements, we obtain a
        structure with the transfer function




            Hence, the transfer function is modified, but now we also interleave the input
        sequence with zeros. The new input sequence becomes



            The output of the pipelined filter becomes



            Hence, the proper output sequence is obtained by decimating the sequence
        Y^z) by a factor two. The maximum sample rate has been increased by a factor
        two, but only every other output value is of interest. In reality we have not gained
        anything. However, two independent sequences can be filtered by the same filter
        as illustrated in Figure 6.55. This technique can be used to map algorithms onto
        systolic and wave front arrays as well as for programming heavily pipelined stan-
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