Introduction to DSP - IIR filters: direct form II

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

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:

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

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'.