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Dyadic Filter Banks

A

*dyadic filter bank*is any

*octave filter bank*,

^{12.6}as illustrated qualitatively in Figure 11.34. Note that is the top-octave bandpass filter, is the bandpass filter for next octave down, is the octave bandpass below that, and so on. The optional scale factors result in the same sum-of-squares for each channel-filter impulse response. A dyadic filter bank may be derived from the discrete wavelet filter bank by setting and relaxing the exact orthonormality requirement on the channel-filter impulse responses. If they do happen to be orthonormal, we may call it a

*dyadic wavelet filter bank*. For a dyadic filter bank, the center-frequency of the th channel-filter impulse response can be defined as

(12.123) |

so that

(12.124) |

Thus, a dyadic filter bank is a special case of a

*constant-Q filter bank*for which the is .

**Next Section:**

Dyadic Filter Bank Design

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Discrete Wavelet Filterbank