Frame analysis of wavelet type filter banks

The discrete wavelet transform, and multiresolution analysis, can be viewed as the application of a non-uniform filter bank. The polyphase matrix representation of the corresponding frame operator is given for general oversampled wavelet-type filter banks. The issue of lower and upper bounds of the frame and their relation to those of the underlying one level filter bank frame is treated, and bounds are given in a few special cases. A few examples are presented demonstrating the use of the results obtained.