An adaptive projection algorithm for multirate filter bank optimization

We develop a new algorithm for multirate filter bank optimization, which finds application in subband coding or wavelet signal analysis. Although some impressive off-line algorithms have recently been developed for this purpose, the computation demand of such algorithms often renders them prohibitive for real-time applications. In this vein, adaptive filtering solutions remain of interest. A simple gradient descent algorithm may be ill suited due to the nonquadratic nature of the cost function to be minimized, and accordingly non gradient algorithms may offer some attractive alternatives. The present paper describes a projection type algorithm, which aims to construct a lossless filter bank such that one of its impulse responses lies close to an extremal eigenvector of the input signal autocorrelation matrix. Though a formal convergence proof of the algorithm is not offered, simulations show that the algorithm converges to an acceptable vicinity of the global minimum point of the cost function.