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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

**Previous Section:**

Discrete Wavelet Filterbank