The design of a pair of orthogonal scaling filters

In this paper we consider designing a scaling filter that is orthogonal to another scaling filter. This is motivated by recent research on the complex wavelet transform and its applications. It is expected that the two wavelet transformations of the same signal using a pair of orthogonal scaling filters will be able to capture different characteristics of the signal. This will open up new pathways for improving the performance of certain wavelet based signal processing techniques. We present design examples using both parameterization for orthogonal wavelets and numerical optimization. We also demonstrate an application of the orthogonal scaling filter pairs in signal denoising.