A fast exhaustive search algorithm for checking limit cycles in fixed-point digital filters

Abstract The presence of limit cycles in fixed arithmetic implementations of digital filters can significantly impair their performances. This paper presents a fast algorithm to determine the presence or absence of such limit cycles and their exact maximum amplitude. This algorithm may be used for different arithmetic representations and for second-order section with one or two quantizers. Computer results are given to establish the feasibility of the algorithm, which may be helpful to designers by providing them a knowledge of when and where he must really resort to more complex filters structures and rounding strategies.

[1]  S. Parker,et al.  Computation of bounds for digital filter quantization errors , 1973 .

[2]  Kamal Premaratne,et al.  An exhaustive search algorithm for checking limit cycle behavior of digital filters , 1996, IEEE Trans. Signal Process..

[3]  W. Mecklenbrauker,et al.  Frequency domain criteria for the absence of zero-input limit cycles in nonlinear discrete-time systems, with applications to digital filters , 1975 .

[4]  ACCESSIBILITY OF ZERO-INPUT LIMIT CYCLES. , 1981 .

[5]  James H. Strickland,et al.  Maximum amplitude zero-input limit cycles in digital filters , 1984 .

[6]  I. Sandberg,et al.  A bound on limit cycles in fixed-point implementations of digital filters , 1972 .

[7]  T. Claasen,et al.  Effects of quantization and overflow in recursive digital filters , 1976 .

[8]  T. Trick,et al.  An absolute bound on limit cycles due to roundoff errors in digital filters , 1973 .

[9]  Debasis Mitra,et al.  Controlled rounding arithmetics, for second-order direct-form digital filters, that eliminate all self-sustained oscillations , 1981 .

[10]  Additional properties of one-dimensional limit cycles , 1986 .

[11]  Parviz Rashidi.  Limit cycle oscillations in digital filters , 1978 .

[12]  Peter H. Bauer,et al.  A computer-aided test for the absence of limit cycles in fixed-point digital filters , 1991, IEEE Trans. Signal Process..

[13]  T. Trick,et al.  A note on absolute bounds on quantization errors in fixed-point implementations of digital filters , 1975 .

[14]  Gian Antonio Mian,et al.  Effects of quantization in second-order fixed-point digital filters with two's complement truncation quantizers , 1988 .