next up previous contents
Next: MPEG-1Layer I and Up: Existing Coders and Standards Previous: Existing Coders and Standards

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:

eqnarray27

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

eqnarray31

To obtain aliasing cancellation, the following is required:

eqnarray39

Optimally,

equation41

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 ):

equation45

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