Linearized least squares design of transformation function for filter banks

The design of biorthogonal filter banks using the transformation of variables technique is considered in this paper. The transformation function is constructed by using the Parametric Bernstein Polynomial and a high number of vanishing moments can be easily achieved. In previous approaches, the transformation function is designed independently of the prototype filter but in this paper the transformation is optimized with regards to the prototype filter. A least squares formulation leads to a complex nonlinear optimization problem. We present a way to linearize the problem and then present an efficient iterative procedure to solve the problem. © 2005 IEEE.