LLL Algorithm and the Optimal Finite Wordlength FIR Design

In practical finite-impulse-response (FIR) digital filter applications, it is often necessary to represent the filter coefficients with a finite number of bits. The finite wordlength restriction increases the filter deviation. This increase can be reduced substantially if the optimal finite wordlength coefficients are used. The time needed to compute these coefficients is greatly reduced with the help of a lower bound on the deviation increase. Derivation of an improved lower bound that uses the well-known LLL algorithm is presented in this correspondence.