Design of multidimensional finite-wordlength FIR and IIR filters by simulated annealing

This paper describes a new approach to the design of multidimensional (M-D) finite-wordlength digital filters with specifications in the frequency and spatial domains. The approach is based on stochastic optimization and extends previous work on finite impulse response (FIR) filters in two ways: by inclusion of spatial constraints and by application to the case of infinite impulse response (IIR) filters. The formulation proposed is based on a multiple-term objective function that, in addition to magnitude constraints, also includes step response, group delay and stability constraints. Our attention to these characteristics stems from the application of such filters to video processing that we are actively pursuing. Since filter coefficients are of finite precision and since the objective function is multivariable, nondifferentiable and likely to have multiple minima, we use simulated annealing for optimization. We show numerous examples of the design of practical filters such as channel and luminance/chrominance separation filters used in the NTSC system. We demonstrate the impact of coefficient precision as well as of group delay and step response constraints on filter parameters. >

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  Thomas S. Huang,et al.  The importance of phase in image processing filters , 1975 .

[3]  Jake K. Aggarwal,et al.  The measurement of phase distortion due to filtering in digital pictures , 1977 .

[4]  M. Fahmy,et al.  Design of two-dimensional recursive digital filters with specified magnitude and group delay characteristics , 1978 .

[5]  C. K. Yuen,et al.  Theory and Application of Digital Signal Processing , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

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

[7]  G. Jullien,et al.  Design of two-dimensional recursive digital filters using linear programming , 1982 .

[8]  Panajotis Agathoklis,et al.  The margin of stability of 2-D linear discrete systems , 1982 .

[9]  Scott Kirkpatrick,et al.  Optimization by Simmulated Annealing , 1983, Sci..

[10]  John W. Woods,et al.  Two-dimensional IIR filter design with magnitude and phase error criteria , 1983 .

[11]  Dan E. Dudgeon,et al.  Multidimensional Digital Signal Processing , 1983 .

[12]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[13]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Moustafa M. Fahmy,et al.  A new technique for the design of two-dimensional FIR and IIR filters , 1985, IEEE Trans. Acoust. Speech Signal Process..

[15]  Jerry C. Whitaker,et al.  Television engineering handbook , 1986 .

[16]  David C. Munson,et al.  FINITE WORD LENGTH FIR DIGITAL FILTER DESIGN USING SIMULATED ANNEALING. , 1986 .

[17]  Tao Lin,et al.  Design of 2-D digital filters with an arbitrary response and no overflow oscillations based on a new stability condition , 1987 .

[18]  William F. Schreiber,et al.  Improvements to NTSC by Multidimensional Filtering , 1988 .

[19]  Joos Vandewalle,et al.  Simulated‐annealing‐based optimization of coefficient and data word‐lengths in digital filters , 1988 .

[20]  Gian Antonio Mian,et al.  Computer aided design of multidimensional FIR filters for video applications , 1989 .

[21]  Michele Marchesi,et al.  Digital filters design by simulated annealing , 1989 .

[22]  N-dimensional symmetries and their applications in digital filters , 1990 .

[23]  Janusz Konrad,et al.  Design of finite wordlength IIR filters with prescribed magnitude, group delay and stability properties using simulated annealing , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[24]  Nevio Benvenuto,et al.  A design technique for two-dimensional multiplierless FIR filters for video applications , 1992, IEEE Trans. Circuits Syst. Video Technol..

[25]  Eric Dubois,et al.  On the design of finite wordlength IIR filters for video applications , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[26]  Michele Marchesi,et al.  Applications of simulated annealing for the design of special digital filters , 1992, IEEE Trans. Signal Process..