## 10.5 PARALLEL PROCESSING FOR IIR FILTERS

In this section, the techniques for parallel processing of IIR filters is discussed. Parallel processing for a simple 1st-order IIR filter is discussed first. After that, parallel processing for higher order filters is discussed.

**Example 10.5.1** *Consider the transfer function of a 1st-order IIR filter given in (10.49)*

*where for stability. This transfer function has only 1 pole located at z = a. The corresponding input output relation can be written as:*

*Consider the design of a 4-parallel architecture (L* = 4*) for the foregoing filter. Note that in the parallel system, each delay element is referred to as a block delay, where the clock period of the block system is 4 times the sample period. Therefore, instead of (10.50), the loop update equation should update y*(*n + 4*) *using inputs and y*(*n*). *By iterating the recursion (in (10.50)) or by applying*

*Fig. 10.14* Single state update operation in a 4-parallel filter.

*look-ahead technique, we get*

*Substituting n = 4**k* in (10.51),

*The corresponding architecture is shown in Fig. 10.14. Notice the ...*