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Digital Filters Design for Signal and Image Processing by Mohamed Najim

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7.3. Structure of IIR filters

7.3.1. Direct structures

In this section, we will refer to the direct canonic structure that is characterized by the following transfer function:

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First, we introduce an intermediary output x1(k), so that:

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The transfer function in equation (7.1) can then be decomposed into a product of two transfer functions:

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All this occurs as if the filter Hz(z) has been obtained by cascading an FIR filter H1(z) and an IIR filter H2(z).

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Figure 7.2. Putting filters H1 and H2 into cascade

We end up with the most spontaneous realization, called the direct form structure 1.

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Figure 7.3. Direct form structure 1 of an IIR filter

We see that this structure requires N+M−2 delay cells. We can then ask the following question: can we share some cells and only use M-l delay cells, knowing that M>N? The answer is yes, leading us to the direct form structure 2.

Figure 7.4. Direct form ...

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