Transforming 1-D even-length filterbanks into 2-D filterbanks

The McClellan transformation is an efficient and flexible technique for designing 2-D filters and filterbanks. The transformation can be naturally applied to 1-D odd-length filters but is harder to apply to even-length filters. Starting with a 1-D filter bank with the perfect reconstruction (PR) property, in general, the PR property is not preserved in the 2-D filterbank if the transformation is performed independently on the individual filters. In this work, we propose a new class of transformation that preserves PR and present examples of such transformation. With the transformations 2-D filterbanks with even support width can be designed with ease.