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Convergence results on adaptive approximate filtering

We present an IIR filtering technique based upon a recently proposed approach for reducing power consumption in implementation of frequency-selective filters. The basic idea in such techniques is to utilize the most recent input and output signal samples to estimate the current SNR (defined as the ratio of the in-band signal power to the out-of-band signal power) at the filter's input. This estimated input SNR is then used to update the filter order to the minimum value which would guarantee a minimum tolerable SNR at the filter's output. A key issue addressed in this paper is how well the estimated filter order converges to the theoretical minimum for situations satisfying the assumptions behind the derivation of the technique. Experimental results are used to verify that convergence to the correct filter order depends (1) upon the number of input and output samples used for estimating the input SNR, (2) upon the filter order applied in generating the output samples that are used in estimating the input SNR and (3) upon the proximity of the actual input SNR to boundaries in the input-SNR space corresponding to changes in the optimal choice for filter order.