Int. Journal of Math. Analysis, Vol. 5, 2011, no. 32, 1583 - 1593 A Construction of a Pairwise Orthogonal Wavelet Frames Using Polyphase Matrix Ghanshyam Bhatt Tennessee State University Department of Physics and Mathematics 3500 John A Merritt Blvd Nashville, TN, 37209, USA gbhatt@Tnstate.edu Abstract This paper surveys the progress made on pairwise orthogonal wavelet frames and comments on the construction methods. There are a few known constructions based on the unitary extension principle, a pa- raunitary matrix and a given modulation matrix. A polyphase matrix based construction method has been presented which satisfies the con- dition of unitary extension principle yielding pairwise orthogonal tight wavelet frames. This enables us to study the approximation and van- ishing moment properties of the resulting frame. Mathematics Subject Classification: 42 Keywords: Wavelets, Frames, Polyphase Components, Orthogonal frames 1 Introduction Over the past few years wavelets and frames have made significant development in theory and applications. In some of the applications wavelet bases have been proven to be better than the classical Fourier basis. Being linearly dependent spanning set, frames generalize the orthonormal basis. Like wavelets, frames have some desirable properties like vanishing moments, compact support, ap- proximation order, symmetry etc. This paper focuses on a pair of orthogonal wavelet frames as characterized in [10]. Following this characterization, a pair of orthogonal wavelet frames are constructed in [1, 6] where the construction is based on modulation matrix. The approximation properties for the wavelet system only depend on the scaling filter whereas in case of frames it depends on how the polyphase matrix is completed [9]. The necessary and sufficient con- ditions for approximation order in multiple spatial dimensions for the wavelet