Telescoping rounding for suboptimal finite wordlength FIR digital filter design
Digital Signal Processing
Discrete-Time Signal Processing
Discrete-Time Signal Processing
IEEE Transactions on Signal Processing
Performance limit of finite wordlength FIR digital filters
IEEE Transactions on Signal Processing
LLL Algorithm and the Optimal Finite Wordlength FIR Design
IEEE Transactions on Signal Processing
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In practical FIR digital filter applications it is often necessary to represent the filter coefficients with a finite number of bits. The optimal finite wordlength coefficients have an interesting property. For all finite wordlength filters there exists a maximum filter length N"m"a"x and the corresponding cosine polynomial degree n"m"a"x. Increasing the filter length N beyond N"m"a"x gives additional coefficients that are all zero. A theoretical explanation for the existence of N"m"a"x is given in the paper. The influence of the filter specifications on N"m"a"x is investigated. In addition, a simple method that gives a reasonably accurate estimate of N"m"a"x is also given. Knowing N"m"a"x and its relationship to the filter specifications is important in the finite wordlength FIR design because it can reduce the time needed to compute the optimal coefficients.