Plotting and Scheming with Wavelets

1. Introduction Wavelets are acquiring a visibility and popularity that may soon be on the scale rst enjoyed by fractals a few years back. Like fractals, wavelets have attractive and novel features, both as mathematical entities and in numerous applications. They are often touted as worthwhile alternatives to classical Fourier analysis, which works best when applied to periodic data: wavelet methods make no such assumptions. However, the mathematics of wavelets can seem intractable to the novice. Indeed, most introductions to wavelets assume that the reader is already well versed in Fourier techniques. Our main goal is simple: to convince the reader that at their most basic level, wavelets are fun, easy, and ideal for livening up dull conversations. We demonstrate how elementary linear algebra makes accessible this exciting and relatively new area at the border of pure and applied mathematics.