### 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

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Filtering and Downsampling