• Summary
• Related Documents
  • Active Bibliography
  • Co-citation
• Version History

Abstract:

We design filter banks that are best matched to input signal statistics in M-channel subband coders, using a rate--distortion criterion. Recent research has shown that unconstrained--length paraunitary filter banks optimized under various energy compaction criteria are principalcomponent filter banks and satisfy two fundamental properties: total decorrelation and spectral majorization. We present several fundamental new results. Firstly, we prove that the two properties above are not specific to the paraunitary case, but are also satisfied for a much broader class of design constraints. Secondly, we prove that optimal perfect--reconstruction filter banks are in the form of the cascade of principal--component filter banks and a bank of pre-- and post--conditioning filters. The proof uses variational techniques and is applicable to a variety of constrained design problems. Thirdly, our results apply to a broad class of rate--distortion criteria, including the conventional coding gain criterion as a special case. Fourthly, we derive analytical expressions for optimal IIR and FIR biorthogonal filter banks by application of the properties above. In the IIR biorthogonal case, our analysis demonstrates the correctness of a recent conjecture by several researchers. The performance loss due to FIR constraints is quantified theoretically and experimentally.

Citations