### Polyphase Decomposition of Haar Example

Let's look at the polyphase representation for this example. Starting with the filter bank and its reconstruction (see Fig.11.17), the polyphase decomposition of is

(12.31) |

Thus, , and therefore

(12.32) |

We may derive polyphase synthesis filters as follows:

*transpose*of the analysis filter bank [263]. A filter bank that is inverted by its own transpose is said to be an

*orthogonal filter bank*, a subject to which we will return §11.3.8.

*STFT filter bank*for , with , and rectangular window . That is, the DFT size, window length, and hop size are all 2, and both the DFT and its inverse are simply sum-and-difference operations.

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Quadrature Mirror Filters (QMF)

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Haar Example