Technical Report Number
In this paper z-transform theory is used to develop the discrete orthonormal wavelet transpform for multidimensional signals. The tone is tutorial and expository. Some rudimentary knowledge of z-transforms and vector spaces is assumed. The wavelet transform of a signal consists of a sequence of inner products of a signal computed against the elements of a complete orthonorml set of basis vectors. The signal is recovered as a weighted sum of the basis vectors. This paper addresses the necessary and sufficient conditions that such a basis muct respect. An algorithm for the design of a proper basis is derived from the orthonormality and perfect reconstruction conditions. In the interest of simplicity the case of multidimensional signals is treated separately. The exposition lays bare the structure of the hardware and software implementations.
Frazier, Michael and Kumar, Arun, "The Discrete Orthonormal Wavelet Transform: An Introduction" Report Number: WUCS-91-30 (1991). All Computer Science and Engineering Research.