Glenn Bradford

A brief survey of a paper by Peter Steffen, et al. Introduction G.K. Chesterton, an English author and journalist from the turn of the century, once stated he desired to write a story about a man setting sail from England in search of a new and foreign land. Eventually, when the man reached the island of his destination, he found it to be the most extraordinary and fascinating place. Unbeknownst to him, though, he had inadvertently returned to England and was merely observing his surroundings with new insight. While the intent of Chesterton's analogy was certainly not related to signal processing, he might as well have been speaking about filter bank theory and the development of wavelet decomposition. Filter bank theory had long been a well explored topic in signal processing when, in the field of mathematics, the idea of decomposing a signal with a wavelet transform was first postulated. The connection between the two has been well studied since, especially in the 2-band filter bank case. This paper will provide an overview of the work done by Peter Steffen et al. in Theory of Regular M-Band Wavelet Bases, a paper that explores using M-band filter banks to create orthogonal wavelet bases. A brief overview of both wavelet decomposition theory as well as Filter Bank theory will be provided, followed by a summary of the main points of the paper.