Symmetric self-Hilbertian filters via extended zero-pinning

A symmetric self-Hilbertian filter is a product filter that can be used to construct orthonormal Hilbert-pair of wavelets for the dual-tree complex wavelet transform. Previously reported techniques for its design does not allow control of the filters frequency response sharpness. The Zero-Pinning (ZP) technique is a simple and versatile way to design orthonormal wavelet filters. ZP allows the shaping of the frequency response of the wavelet filter by strategically pinning some of the zeros of the parametric Bernstein polynomial. The non-zero Bernstein parameters, αi s, are the free-parameters and are constrained in number to be twice the number of pinned zeros in ZP. An extension to ZP is presented here where the number of free-parameters is greater than twice the number of pinned zeros. This paper will show how the extended ZP can be used to the design of Hilbert pairs with the ability to shape the filter response. © 2011 Elsevier B.V. All Rights Reserved.