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## How to make wavelets from filters

### Iain Raeburn

University of Newcastle, Australia

###
Thursday, November 17, 2005

L01 Carson Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: ** A wavelet is a function whose dilates and
translates form an orthonormal basis for *L^2(***R**). Wavelets
have proved to be enormously useful in both theory and applications,
and hence there has been a great deal of interest in methods of
constructing wavelets. One famous construction of Mallat starts from a
filter, which is a function defined on the unit circle. In this talk
we will show how some basic ideas from abstract algebra and the
geometry of Hilbert space make Mallat's construction seem very
natural, and in particular explain how it is that a function on the
circle can give rise to a basis for functions on the real line.

Any new ideas in this talk are joint work with Nadia Larsen of the
University of Oslo.

This talk will be accessible to graduate students.