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FIR filter design, Finite Wordlength Coefficients, Babai's Algorithm, LLL Algorithm, Closest Vector Problem

Optimal finite linear-phase impulse response (FIR) filters are most often designed using the Remez algorithm, which computes so-called infinite precision filter coefficients. In many practical applications, it is necessary to represent these coefficients by a finite number of bits. The problem of finite wordlength linear-phase filters is not as trivial as it would seem. The simple rounding of coefficients computed by the Remez algorithm gives us a suboptimal filter. Optimal finite wordlength linear-phase FIR filters are usually designed using integer linear programming, which takes a lot of time to compute the coefficients. In this paper, we introduce a new approach to the design of finite wordlength FIR filters using very fast Babai's algorithm. Babai's algorithm solves the closest vector problem, and it uses the basis reduced by the LLL algorithm as an input. We have used algorithms which solve the problem in the L2 norm and then added heuristics that improve the results relative to the L? norm. The design method with Babai's algorithm and heuristics has been tested on filters with different sets of frequency-domain specifications.