6 Memory Requirements 7.1 Uniform Filter Banks 7.2 Wavelet Filter Banks 7.3 Final Notes

8 system, closely models the critical bands of human hearing. Filter design methods were shown for the octave band lters and the third octave lters, as well as calculating the corresponding costs in latency, memory and complexity. In this system, the amount of memory required comes from two places: the delay lines inserted into the DTWT to ensure subband time synchronization , and the FIR lters inside the third octave QMF lter banks. For the DTWT, the memory needed for the inserted delay line lengths increases exponentionally for the number of octaves K: (2 K ? (K + 1)))L + D third ] which comes to 10,374 samples in this design. The number of memory required by the lowpass and highpass lters for the DTWT is 4L(K +1), which is 1,260 samples for this system. For the third octave sections, memory is needed for the polyphase ltering within the QMF banks. A cosine modulated QMF analysis bank of length N prototype lowpass lter requires N elements of delay, while a synthesis bank requires twice as much memory, 2N samples. For K octaves, it can be shown that this memory tallies to 6192(K+1), which amounts to 6,912 samples. Thus, for all of the previous sources of memory, the entire system requires 18,546 samples of memory. 7 Comparisons to other Filter Banks There are many other time-frequency representations used in audio data compression, using both uniform and nonuniform lter banks. In this section , we will attempt to just name a few. The most widely used audio coding algorithms today, MPEG Brandenburg and Stoll, 1994] and AC-3 Todd, 1994], both use variations of uniform, cosine modulated lapped transforms Malvar, 1992]. MPEG uses a 512 point window with a 32 point transform Rothweiler, 1983], while AC-3 uses a 512 point window with a 256 point transform Princen, 1987]. Both systems use some form of window length adaptation to compensate for pre-echo eeects during transients. These commercial lter banks were primarily chosen due to their low complexity and their low memory requirements, which are large factors when implementing these solutions in hardware. In exchange, the lter banks do not match the critical bands of hearing. A recent study in nonuniform lter banks for audio coding was presented by Sinha and Tewwk, 1993]. They implemented an 8 stage, 29 subbands wavelet packet representation using uniform, two channel FIR lters at each node of the tree. …