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Subband Coders

  Subband splitting of a signal is often performed with a two-channel uniform filterbank. The filterbank is used several times to achieve finer bandsplitting, in a filter tree:


This way, the coder can split the input data into uniform bands, in each of which a quantizer, adopted to the masking threshold (see section 3), is applied.

The filterbank filterbank consists of four filters, tex2html_wrap_inline942 , tex2html_wrap_inline944 , tex2html_wrap_inline946 and tex2html_wrap_inline948 . The F's are used to split the input data in a high and a low frequency band. Both bands are then subsampled with a factor of 2. To reconstruct, both bands are upsampled again, and filtered with the G's. Thus, the output tex2html_wrap_inline954 can be written as


To obtain aliasing cancellation, the following is required:




so that perfect reconstruction is achieved. This is, though, often hard to achieve. The filters used in most coders are Quadrature Mirror Filters (QMF), which achieve aliasing cancellation by choosing tex2html_wrap_inline956 as the mirror image of tex2html_wrap_inline958 (around tex2html_wrap_inline960 ):


To get good reconstruction without relying on the aliasing cancellation, which does not work perfectly in the presence of quantization noise, the QMF filters have to have a steep pass-to-stop-band transition.

Bosse Lincoln
Sat Mar 7 16:27:43 PST 1998