# 6.7 M-channel filter banks

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The theory of M-band QMFBs and PRFBs has been investigated recently. Some results are available.

## Tree-structured filter banks

Once we have a two-band PRFB, we can continue to split the subbands with similar systems! ( [link] )

Thus we can recursively decompose a signal into $2^{p}$ bands, each sampled at $2^{p}$ th the rate of the original signal, and reconstruct exactly! Due to the tree structure, this can be quiteefficient, and in fact close to the efficiency of an FFT filter bank, which does not have perfect reconstruction.

## Wavelet decomposition

We need not split both the upper-frequency and lower-frequency bands identically. ( [link] )

This is good for image coding, because the energy tends to be distributed such that after a wavelet decomposition, each bandhas roughly equal energy.

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