A direct method for the design of 2-D nonseparable filter banks

A direct approach for the design of 2-D nonseparable diamond-shaped filter banks is proposed. The design goal is achieved by formulating the problem as an iterative quadratic programming problem in which the perfect reconstruction condition is incorporated in a weighted quadratic objective function. Satisfactory stopband attenuation is assured by imposing a set of constraints on the amplitude response of the low-pass analysis filter. Formulas for the exact and efficient evaluation of the objective function are derived, which facilitate precise and efficient function evaluations. The authors conclude with two design examples that illustrate the proposed design method.