(picture obtained from www.gvsu.edu/mathstat/wavelets/hill.htm)
The next known link to wavelets came from a man named Alfred Haar in the
year 1909. It appeared in the appendix of a thesis he had written
to obtain his doctoral degree.
Alfred
Haar was born on October 11, 1885 in Budapest, Hungary. In 1904,
Haar traveled to Germany to study at Gottingen where he studied under Hilbert
[4]. It was here where his doctoral thesis work was done on the orthogonal
systems of functions. Unlike Fourier, Haar spent the better part
of his career either studying mathematics or teaching it. He died
March 16, 1933 in Szeged, Hungary.
Haar’s contribution to wavelets is very evident. There is an entire
wavelet family named after him. The Haar wavelets are the simplest
of the wavelet families. The concept of a wavelet family is easy
to understand. The father wavelet (scaling function) is the starting
point (head of the household in a matter of speaking). By scaling
and translating the father wavelet, we obtain the mother, daughters, sons,
granddaughters, grandsons, etc. Below is an example of the Haar father
wavelet
(picture obtained from www.gvsu.edu/mathstat/wavelets/hill.htm)