Design and convergence analysis of a multirate structure for adaptive filtering

A Multi-Rate (MR) Adaptive Filtering Structure (AFS) that identifies the Generalised Polyphase Components (GPCs) of the Polyphase Components (PCs) of an unknown system is proposed. This new method consists of incorporating the Generalised Structural Subband Decomposition (GSSD) in the subband signals of an MR structure to increase the Convergence Rate (CR) when the input signal is coloured. The increase in the CR comes practically at no expense to the computational complexity. A new result related to Cosine Modulated (CM) Filter Banks (FBs) is given which is then used to show that the introduced generalisation does not affect the performance of the structure when the input signal is white. Experimental results show the improvement in the performance resulting from the proposed modifications.