Wavelets provide an alternative to classical Fourier methods for one- and multi-dimensional data analysis and synthesis, and are better suited to data which lack periodicity or contain sudden changes.
This talk will introduce the basics of wavelets via a popular application
to compression of images, data and audio. Prerequisites will be kept
to a minimum: anybody who can add, subtract and divide by two should feel
quite at home.
We'll show how to combine simple ideas
from linear algebra and multivariable calculus to explore a wide class
of interesting curves and surfaces, using basic polynomial and piecewise-polynomial
methods. A frequent goal is data fitting, whether exact (interpolation)
or approximate (Bezier or least squares methods), and a popular approach
is to use splines. Computer algebra systems such as Maple
can be used to take the drudgery out of the algebraic manipulations and
provide immediate visual access to the shapes which result.