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Introduction to DSP - IIR filters: direct form II

The filter diagram for direct form 1 can be drawn direct from the filter equation:

Filter equation block diagram

The block diagram is in two halves: and since the results from each half are simply added together it does not matter in which order they are calculated. So the order of the halves can be swapped:

Filter equation block diagram

Now, note that the result after each delay is the same for both branches. So the delays down the centre can be combined:

Filter equation block diagram

This is called direct form 2. Its advantage is that it needs less delay elements. And since delay elements require hardware (for example, processor registers) the direct form 2 requires less hardware and so is more efficient than direct form I.

direct form 2 is also called canonic, which simply means 'having the minimum number of delay elements'.

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