#### 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