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

.
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