A Lattice Basis Reduction Approach for the Design of Quantized FIR Filters

Nicolas Brisebarre (1, 2) , Silviu-Ioan Filip (2) , Guillaume Hanrot (2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 ARIC - Arithmetic and Computing

Many applications of finite impulse response (FIR) digital filters impose strict format constraints for the filter coefficients. Such requirements increase the complexity of determining optimal designs for the problem at hand, making exact approaches intractable even for moderately high filter degrees. We introduce a fast and efficient heuristic, which is based on the computation of good nodes for polynomial interpolation and Euclidean lattice basis reduction. Most of the time, it returns quantized FIR filters of extremely good quality.

Mots clés: minimax approximation; LLL algorithm; lattice basis reduction; HKZ algorithm; FIR digital filters; finite wordlength; FIR coefficient quantization; Euclidean Lattice; Index Terms—BKZ algorithm

Domaines: Arithmétique des ordinateurs; Traitement du signal et de l'image [eess.SP]

Nicolas Brisebarre, Silviu-Ioan Filip, Guillaume Hanrot. A Lattice Basis Reduction Approach for the Design of Quantized FIR Filters. 2016. ⟨hal-01308801v1⟩