m12775 M-Channel Filter Banks 1.3 2005/02/16 21:37:15 US/Central 2009/06/03 16:04:19.034 GMT-5 Douglas L. Jones Douglas L. Jones dl-jones@uiuc.edu Douglas L. Jones Douglas L. Jones dl-jones@uiuc.edu Charlet Reedstrom Charlet Reedstrom charlet@rice.edu Kyle Evan Clarkson Kyle Clarkson kclarks@gmail.com Douglas L. Jones Douglas L. Jones dl-jones@uiuc.edu multirate signal processing Science and Technology en Quadrature Mirror Filterbanks (QMF) Digital Signal Processing (Ohio State EE700)` Digital Filter Design Adaptive Filters Digital Filter Structures and Quantization Error Analysis The DFT, FFT, and Practical Spectral Analysis The theory of M-band QMFBs and PRFBs has been investigated recently. Some results are available.

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

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 quite efficient, and in fact close to the efficiency of an FFT filter bank, which does not have perfect reconstruction.

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

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