Parallel Form

In the canonical parallel form, the transfer function H(z) is expanded into partial fractions. H(z) is then realized as a sum of a constant, first-order, and second-order transfer functions as shown below.

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This expansion, where K is a constant and the  are the first and second-order transfer functions, is shown below.

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As in the series canonical form, there is no unique description for the first-order and second-order transfer function. Due to the nature of the FixPt Sum block, the ordering of the individual filters doesn't matter. However, because of the constant K, the first-order and second-order transfer functions can be chosen such that their forms are simpler than those for the series cascade form described in the preceding section. This is done by expanding H(z) as

The first order diagram for H(z) is shown below.

The second order diagram for H(z) is shown below.

The parallel form example transfer function is given by

The realization of H_ex(z) using the Fixed-Point Blockset is shown below. You can display this model by typing

fxpdemo_parallel_form

at the MATLAB command line.