Finite precision error analysis of a QR-decomposition-based lattice predictor

Abstract

We analyze the finite precision properties ofa QR-decomposition-based adaptive lattice filter used as a linear one-step predictor implemented using fixed-point arithmetic. We present equations for the steadystate mean-squared values of the accumulated numerical errors in the computations of the algorithm. Our analysis indicates that the numerical inaccuracy associated with some of the variables in the algorithm increases with increasing values of the exponential weighting factor employed by the adaptive filter. However, there are some other variables whose numerical accuracy increases with increasing values of the exponential weighting factor, indicating that different variables in the algorithm may need to be implemented with different precisions to obtain the desired numerical accuracy. The analysis also shows that the numerical errors, in general, increase from stage to stage. The errors tend to be larger for highly correlated signals than for signals with less correlation between neighboring samples. We also present experimental verification of the analytical results. The predicted and experimental results show close agreement for practical values of the weighting factor and precision used in the implementation of the adaptive filter.