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

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
.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University