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