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


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Dyadic Filter Bank Design
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Discrete Wavelet Filterbank