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.

[1]  T. Parks,et al.  A program for the design of linear phase finite impulse response digital filters , 1972 .

[2]  Dusan M. Kodek.  Performance limit of finite wordlength FIR digital filters , 2005, IEEE Transactions on Signal Processing.

[3]  M. R. Rao,et al.  Combinatorial Optimization , 1992, NATO ASI Series.

[4]  Dusan M. Kodek.  An algorithm for the design of optimal finite word-length FIR digital filters , 1980, ICASSP.

[5]  M. Powell,et al.  Approximation theory and methods , 1984 .

[6]  Shafi Goldwasser,et al.  Complexity of lattice problems - a cryptographic perspective , 2002, The Kluwer international series in engineering and computer science.

[7]  Nigel P. Smart,et al.  The Algorithmic Resolution of Diophantine Equations: Computational diophantine approximation , 1998 .

[8]  Alan N. Willson,et al.  A trellis search algorithm for the design of FIR filters with signed-powers-of-two coefficients , 1996, Proceedings of the 39th Midwest Symposium on Circuits and Systems.

[9]  K. Steiglitz,et al.  An easily computed performance bound for finite wordlength direct-form FIR digital filters , 1982 .

[10]  Kenneth Steiglitz,et al.  Comparison of optimal and local search methods for designing finite wordlength FIR digital filters , 1981 .

[11]  S. Goldwasser,et al.  Closest Vector Problem , 2002 .

[12]  Dusan M. Kodek.  Limits of finite wordlength FIR digital filter design , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[13]  Marjan Krisper,et al.  Telescoping rounding for suboptimal finite wordlength FIR digital filter design , 2005, Digit. Signal Process..

[14]  A. Constantinides,et al.  Finite word length FIR filter design using integer programming over a discrete coefficient space , 1982 .

[15]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[16]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[17]  J. McClellan,et al.  Complex Chebyshev approximation for FIR filter design , 1995 .

[18]  K. Steiglitz,et al.  Filter-length word-length tradeoffs in FIR digital filter design , 1980 .

[19]  Yong Ching Lim,et al.  Signed power-of-two term allocation scheme for the design of digital filters , 1999 .

[20]  D. Kodek.  Design of optimal finite wordlength FIR digital filters using integer programming techniques , 1980 .

[21]  N. Smart.  The Algorithmic Resolution of Diophantine Equations: S -unit equations , 1998 .

[22]  Y. Lim,et al.  FIR filter design over a discrete powers-of-two coefficient space , 1983 .