### Parallel Case

Figure 6.2 illustrates the

*parallel combination*of two filters. The filters and are driven by the

*same*input signal , and their respective outputs and are

*summed*. The transfer function of the parallel combination is therefore

*z*transform to have that .

#### Series Combination is Commutative

Since multiplication of complex numbers is commutative, we have*numerical*performance of the overall filter is usually affected by the ordering of filter stages in a series combination [103]. Chapter 9 further considers numerical performance of filter implementation structures. By the convolution theorem for

*z*transforms, commutativity of a product of transfer functions implies that

*convolution is commutative*:

**Next Section:**

Example

**Previous Section:**

Series Case