A block floating-point realization of the gradient adaptive lattice filter

We present a novel scheme to implement the gradient adaptive lattice (GAL) algorithm using block floating point (BFP) arithmetic that permits processing of data over a wide dynamic range at a cost significantly less than that of a floating point (FP) processor. Appropriate formats for the input data, the prediction errors, and the reflection coefficients are adopted, taking care so that for the prediction errors and the reflection coefficients, they remain invariant to the respective order and time update processes. Care is also taken to prevent overflow during prediction error computation and reflection coefficient updating by using an appropriate exponent assignment algorithm and an upper bound on the step-size mantissa.