Methods for the design of 2D non-separable filters using semi-definite programming (SOP) with frequency mask constraints are capable of handling filters of very small and moderate sizes. In this paper, the authors propose a new technique for the design of linear phase 2D FIR filter subject to frequency mask constraints, which can handle filters of sufficiently large sizes for practical applications. The designed 2D filters admit a fast digital implementation. Using the notion of 2D trigonometric curves, the authors obtain an 2D trigonometric result to enable the 2D filter specifications to be expressed as semidefinite constraints. As a result, the 2D filter design problem is then posed as SOP. Moreover, the study exploited convex duality to derive equivalent SOP formulation of reduced constraints. Simulation illustrating the advantages of our method for design of ellipse-shaped 2D-filters is presented.