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