Filter bank optimization with applications in noise suppression and communications

Filter banks (FBs) are used in digital signal processing (DSP) for decomposing signals into several frequency bands, which are processed separately and then combined. This allows allocation of processing resources based on the distribution of the relevant signal features among the bands, yielding improved system performance over direct processing of the input signal. FBs are used in almost every area of modern DSP, including audio, image and video compression and communications.; This thesis deals mainly with optimization of FBs based on the statistics of their input. We establish the optimality of a type of FB called the principal component filter bank (PCFB) for numerous signal processing problems. The PCFB depends on the input power spectrum and on the class of M-channel orthonormal FBs over which we seek the best FB. PCFB optimality for compression and progressive transmission has been observed earlier. We provide a unified framework for orthonormal FB optimization, that includes these earlier results as special cases. One of our central results in this context is that PCFBs are optimum orthonormal FBs whenever the minimization objective is a concave function of the vector of subband variances of the FB. Besides data compression, this covers many other signal processing problems not observed earlier. One of them is white noise suppression using subband Wiener filters or hard thresholds. Another example involves power constrained bitrate maximization in discrete multitone modulation (DMT) communication systems, used in ADSL and wireless OFDM technologies. We show that the system performance is improvable at increased implementation cost by replacing traditionally used DFT FBs with PCFBs associated with a certain normalized noise spectrum. The improvement is quantified by simulations with realistic ADSL channel and noise models.; We study various nontrivial extensions of the basic PCFB optimality result to colored noise suppression and to optimization of biorthogonal and nonuniform FBs. Lastly, we also examine a related open problem on the parameterization of nonuniform perfect reconstruction (PR) FBs. We seek necessary and sufficient conditions on a set of decimators for existence of a rational PRFB using those decimators. We strengthen considerably the known conditions, thus contributing an important first step towards a complete PR theory for nonuniform FBs.