SDP for 2-d Filter Design: General Formulation and Dimension Reduction Techniques

In this paper, a new technique for designing linear phase 2-D filter based on semi-definite programming (SDP) is proposed. This approach allows the design of 2-D filters with accurate cut-off frequency, subject to hard bounds on the frequency response to be achieved on a standard computer. Using the notion of 2-D trigonometric curves, we generalize the 2-D trigonometric Markov-Lukacs theorem to identify the pass-band and the stop-band in the region of support. The 2-D filter specifications are expressed as linear matrix inequalities. We also exploit convex duality to derive SDP formulations of reduced dimensions. Numerical examples illustrating the advantages of our method are also presented

[1]  Thomas F. Quatieri,et al.  McClellan transformations for two-dimensional digital filtering. I - Design , 1976 .

[2]  P. P. Vaidyanathan,et al.  Multidimensional multirate filters and filter banks derived from one-dimensional filters , 1993, IEEE Trans. Signal Process..

[3]  R. M. Mersereau,et al.  McClellan transformations for two-dimensional digital filtering-Part I: Design , 1976 .

[4]  Truong Q. Nguyen,et al.  LMI characterization for the convex hull of trigonometric curves and applications , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[5]  P. P. Vaidyanathan,et al.  Recent developments in multidimensional multirate systems , 1993, IEEE Trans. Circuits Syst. Video Technol..

[6]  Hugo J. Woerdeman,et al.  Positive extensions, Fejér-Riesz factorization and autoregressive filters in two variables , 2004 .

[7]  Dimitri Peaucelle,et al.  SEDUMI INTERFACE 1.02: a tool for solving LMI problems with SEDUMI , 2002, Proceedings. IEEE International Symposium on Computer Aided Control System Design.

[8]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[9]  Gian Antonio Mian,et al.  Characteristics of minimax FIR filters for video interpolation/decimation , 1994, IEEE Trans. Circuits Syst. Video Technol..

[10]  Jorge Herbert de Lira,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[11]  Charng-Kann Chen,et al.  McClellan transform based design techniques for two-dimensional linear-phase FIR filters , 1994 .

[12]  HettichR.,et al.  Semi-infinite programming , 1979 .

[13]  C. Guillemot,et al.  Two-dimensional filters with wideband circularly symmetric frequency response , 1994 .

[14]  Kenneth O. Kortanek,et al.  Semi-Infinite Programming: Theory, Methods, and Applications , 1993, SIAM Rev..

[15]  Minh N. Do,et al.  Multidimensional orthogonal filter bank characterization and design using the Cayley transform , 2005, IEEE Transactions on Image Processing.