LMI Approach to Stability of Direct Form Digital Filters Utilizing Single Saturation Overflow Nonlinearity

A criterion for the elimination of limit cycles in direct form digital filters utilizing single saturation overflow nonlinearity is presented. The criterion takes the form of linear matrix inequality and, hence, is computationally tractable. An example showing the effectiveness of the present criterion is given.

[1]  Takao Hinamoto,et al.  Minimization of L/sub 2/-sensitivity for state-space digital filters subject to L/sub 2/-dynamic-range scaling constraints , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Truong Q. Nguyen,et al.  Low-order IIR filter bank design , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Michael G. Taylor,et al.  Overflow oscillations in digital filters , 1969 .

[4]  Jean H. F. Ritzerfeld.  Noise gain expressions for low noise second-order digital filter structures , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Irwin W. Sandberg.  The zero-input response of digital filters using saturation arithmetic , 1979 .

[6]  Kok Lay Teo,et al.  Digital Laguerre filter design with maximum passband-to-stopband energy ratio subject to peak and Group delay constraints , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Håkan Johansson,et al.  Minimax design of adjustable-bandwidth linear-phase FIR filters , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Tzi-Dar Chiueh,et al.  A Low-Power Digit-Based Reconfigurable FIR Filter , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  T. Hinamoto.  Minimization of L_2-sensitivity for state-space digital filters subject to L_2-dynamic-range scaling constraints , 2005 .

[10]  Shing-Chow Chan,et al.  Design of complex-valued variable FIR digital filters and its application to the realization of arbitrary sampling rate conversion for complex signals , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Shlomo Engelberg.  A more general approach to the filter sharpening technique of Kaiser and Hamming , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[12]  S. C. Dutta Roy.  Impulse Response of FIR Filters , 2006 .

[13]  Alfonso Fernández-Vázquez,et al.  A new method for the design of IIR filters with flat magnitude response , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Keshab K. Parhi,et al.  Low- Cost Parallel FIR Filter Structures With 2-Stage Parallelism , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  I. W. Sandberg,et al.  A separation theorem for finite precision digital filters , 1995 .

[16]  A. Michel,et al.  Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters , 1992 .

[17]  Vimal Singh,et al.  Lyapunov-based proof of Jury - Lee's criterion: Some appraisals , 1985 .

[18]  Kaushik Roy,et al.  CSDC: a new complexity reduction technique for multiplierless implementation of digital FIR filters , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Yue-Dar Jou,et al.  Least-Squares Design of FIR Filters Based on a Compacted Feedback Neural Network , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  Debasis Mitra.  The absolute stability of high-order discrete-time systems utilizing the saturation nonlinearity , 1978 .

[21]  Soo-Chang Pei,et al.  Minimum-Phase FIR Filter Design Using Real Cepstrum , 2006 .

[22]  Xiaoping Lai.  Projected least-squares algorithms for constrained FIR filter design , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[23]  Kok Lay Teo,et al.  A weighted least squares approach to the design of FIR filters synthesized using the modified frequency response masking structure , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[24]  Chip-Hong Chang,et al.  Contention resolution algorithm for common subexpression elimination in digital filter design , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[25]  Haranath Kar,et al.  Elimination of overflow oscillations in digital filters employing saturation arithmetic , 2005, Digit. Signal Process..

[26]  Pavel Zahradnik,et al.  An analytical procedure for critical frequency tuning of FIR filters , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[27]  Tanja Karp,et al.  Performance analysis and prototype filter design for perfect-reconstruction cosine-modulated filter banks with fixed-point implementation , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  V. Singh.  A generalized approach for the absolute stability of discrete-time systems utilizing the saturation nonlinearity, based on passivity properties , 1990 .

[29]  I. W. Sandberg,et al.  A separation theorem for finite-precision digital systems , 1997 .

[30]  Kok Lay Teo,et al.  Variable Digital Filter With Least-Square Criterion and Peak Gain Constraints , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[31]  Shing-Chow Chan,et al.  Design of Constrained Causal Stable IIR Filters Using a New Second- Order-Cone-Programming-Based Model-Reduction Technique , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[32]  V. Singh,et al.  Stability analysis of discrete-time systems in a state-space realisation with state saturation nonlinearities: linear matrix inequality approach , 2005 .

[33]  Leland B. Jackson,et al.  Approximating Noncausal IIR Digital Filters Having Arbitrary Poles, Including New Hilbert Transformer Designs, Via Forward/Backward Block Recursion , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[34]  Vimal Singh.  Modified Form of Liu-Michel's Criterion for Global Asymptotic Stability of Fixed-Point State-Space Digital Filters Using Saturation Arithmetic , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[35]  Yue-Dar Jou.  Design of Real FIR Filters With Arbitrary Magnitude and Phase Specifications Using a Neural-Based Approach , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[36]  Guoan Bi,et al.  An improved /spl rho/DFIIt structure for digital filters with minimum roundoff noise , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[37]  A. Michel,et al.  Dynamical Systems with Saturation Nonlinearities: Analysis and Design , 1994 .

[38]  Tatsushi Ooba,et al.  Stability of linear discrete dynamics employing state saturation arithmetic , 2003, IEEE Trans. Autom. Control..

[39]  José Claudio Geromel,et al.  Joint Optimal Design of Digital Filters and State-Space Realizations , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[40]  T. Ooba,et al.  On companion systems with state saturation nonlinearity , 2003 .

[41]  Tian-Bo Deng.  Design of complex-coefficient variable digital filters using successive vector-array decomposition , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

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

[43]  Ying Wei,et al.  A computationally efficient nonuniform FIR digital filter bank for hearing aids , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[44]  E. I. Jury,et al.  On the stability of a certain class of nonlinear sampled-data systems , 1964 .

[45]  Suhash C. Dutta Roy.  Impulse response of sinc/sup N/ FIR filters , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[46]  Zixue Zhao.  An Efficient State-Space Realization With Minimum Roundoff Noise Gain , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[47]  E. I. Jury,et al.  On the absolute stability of nonlinear sample-data systems , 1964 .

[48]  Vimal Singh,et al.  Elimination of overflow oscillations in fixed-point state-space digital filters with saturation arithmetic: an LMI approach , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[49]  Pavel Zahradnik,et al.  Note on the Design of an Equiripple DC-Notch FIR Filter , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.