On the selection and design of filter banks in normalised subband adaptive filters (NSAF)

In this paper we reexamine a popular class of adaptive filter algorithms, namely the Normalised Subband Adaptive Filters (NSAF) whose superior convergence properties in the literature is attributed to the whitening of the input signal through the filter bank used. This viewpoint - by all means a valid one - makes it difficult to relate the convergence behavior of the NSAF directly and quantitatively to the characteristics of the filter banks employed. In continuation of our previous recent work [1], we show how a given filter bank can be quantitatively evaluated with respect to its convergence speed when applied in an NSAF setting. Following this, we explain how optimized filter banks for the NSAF can be designed given more or less accurate knowledge of the correlation properties of the adaptive filter's possible input signals. We present simulation results illustrating our findings and also present some new insights indicating that the range of filter banks that can successfully be employed in NSAFs is wider than what is implied in the literature so far.