Design of signal-adapted nonuniform filter banks using tree structure

Existence of a principal component filter bank (PCFB) for a given class of uniform filter banks has been well studied and optimization algorithms for realisable signal adapted filter banks have already been developed. In this paper we present optimization algorithm for maximally decimated nonuniform finite impulse response (FIR) filter banks that is derived from tree structure. Here PCFB for a class of unconstrained nonuniform orthonormal filter bank is defined using normalised subband variances. This definition results in PCFB optimality for certain types of concave objectives whose form is more restricted. Each unit of tree structure is simulated using iterative greedy algorithm. Simulated filter responses for an input power spectral density (psd) closely match the ideal nonuniform brick-wall responses