### Parallel Second-Order Signal Flow Graph

Figure 3.25 shows the signal flow graph for the implementation of our example filter using parallel second-order sections (with one first-order section since the number of poles is odd). This is the same filter as that shown in Fig.3.1 with , , , and . The second-order sections are special cases of the ``biquad'' filter section, which is often implemented in software (and chip) libraries. Any digital filter can be implemented as a sum of parallel biquads by finding its transfer function and computing the partial fraction expansion.*Transposed*Direct-Form II (TDF-II) is usually a better choice of implementation structure for IIR filters when numerical dynamic range is limited (as it is in fixed-point ``DSP chips''). Figure 3.26 shows how our example looks using TDF-II biquads in place of the DF-II biquads of Fig.3.25.

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