Critically Sampled Third Octave Filter Banks

the complexity of splitting a single fullrate signal into third octave sections. The complexity of a single PQMF cosine modulated lter bank (analysis or synthesis), C QMF (M; N) is on the order of N+MlogM M , where N is the length of the lowpass prototype lter and M is the number of channels in the lter bank. The M in the denominator is because of the dec-imation by M, N is the cost of FIR convolution, and MlogM is the cost of the cosine modulation using fast DCT's. In the forward third octave splitter, as pictured in gure 4, there is not just one QMF bank, but four. The leftmost bank splits the input into 24 signals, each downsampled by 24. To compensate for this diierent sampling rate, the complexities of the three synthesis lter banks must be scaled by a factor of M i