A novel approach to the design of the class of triplet halfband filterbanks

A new approach is presented for designing the recently introduced class of triplet halfband filterbank which are defined by three kernels. The Parametric Bernstein Polynomial is used to construct the kernels. The filterbanks have the advantage of structural perfect reconstruction and structural regularity. The design of the free parameters of the Bernstein Polynomial is achieved through a least squares method. A novel iterative procedure is employed to optimize the objective function which is a multiquadratic function of the free parameters. The design technique is flexible in that it allows filters with different characteristics to be designed with ease. Filter regularity can be traded for increased sharpness in the frequency response and regular scaling function and wavelets can be readily obtained.