document: On biorthogonal nonuniform filter banks and tree structures This paper concerns biorthogonal nonuniform filter banks . It is shown that a tree structured filter bank is biorthogonal if it is equivalent to a tree structured filter bank whose matching constituent levels on the analysis and synthesis sides are themselves biorthogonal pairs . We then show that a stronger statement can be made about dyadic filter banks in general : That a dyadic filter bank is biorthogonal if both the analysis and synthesis banks can be decomposed into dyadic trees . We further show that these decompositions are stability and FIR preserving . These results , derived for filter banks having filters with rational transfer functions , thus extend some of the earlier comparable results for orthonormal filter banks
doc_bio_tags: O B I I I O O O O O O B I I I O O O O O O B I I I O O O O O O O O B I I I O O O O O O O O O O O O B I O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O B I I O O O O O O O O O O O O O
extractive_keyphrases: biorthogonal nonuniform filter banks tree structured filter bank biorthogonal pairs dyadic filter banks dyadic trees fir preserving rational transfer functions
abstractive_keyphrases: stability preserving