### Two-Channel Case

The simplest nontrivial case is channels. Starting with a general linear time-invariant filter

 (12.6)

we may separate the even- and odd-indexed terms to get

 (12.7)

We define the polyphase component filters as follows:

and are the polyphase components of the polyphase decomposition of for . Now write in terms of its polyphase components:

 (12.8)

As a simple example, consider

 (12.9)

Then the polyphase component filters are

and

 (12.10)

Next Section:
N-Channel Polyphase Decomposition
Previous Section:
Filtering and Downsampling