The last wavelet researcher that we will discuss is Ingrid Daubechies, who is currently a professor at Princeton University. She was born in Houthalen, Belgium and earned her Ph. D in Physics in 1980. She is the first full female professor for Princeton University.
Around 1988, Daubechies used the idea of multiresolution analysis to create her own family of wavelets. These wavelets were of course named the Daubechies Wavelets. Daubechies wavelet family satisfies a number of wavelet properties. They have compact support, orthogonality, regularity, and continuity. We will be able to recognize their compact support in the following example. The property of orthogonality is satisfied because the inner products of all of the various translates of the Daubechies wavelets are zero. The regularity property is satisfied because the Daubechies wavelets can reproduce linear functions. Finally, the continuity property is satisfied because the Daubechies wavelet functions are continuous even though they are not very smooth and not differentiable everywhere. Although its not a very good one, there is an example of the Daubechies scaling function shown below.
