#### Discrete Wavelet Filterbank

In a *discrete wavelet filterbank*, each basis signal is
interpreted as the impulse response of a bandpass filter in a
constant-Q filter bank:

Thus, the th channel-filter is obtained by

*frequency-scaling*(and normalizing for unit energy) the zeroth channel filter . The frequency scale-factor is of course equal to the inverse of the time-scale factor.

Recall that in the STFT, channel filter
is a *shift* of
the zeroth channel-filter
(which corresponds to ``cosine
modulation'' in the time domain).

As the channel-number increases, the channel impulse response lengthens by the factor ., while the pass-band of its frequency-response narrows by the inverse factor .

Figure 11.32 shows a block diagram of the discrete wavelet
filter bank for
(the ``dyadic'' or ``octave filter-bank'' case),
and Fig.11.33 shows its time-frequency tiling as compared to
that of the STFT. The synthesis filters
may be used to make
a *biorthogonal* filter bank. If the
are orthonormal, then
.

**Next Section:**

Dyadic Filter Banks

**Previous Section:**

Discrete Wavelet Transform