The Haar vector space V_{2 }has dimension 4. One basis for V_{2 } is B_{2 } = {f, y, y_{1,0},y_{1,1}}. Based on a suggestion by Prof. David Hill of Temple University, here are the graphs of these four functions, along with a table of their inner products.
A Basis for V_{2}
The Haar father wavelet f

The Haar mother wavelet y

The Haar daughter wavelet y_{1,0}

The Haar daughter wavelet y_{1,1} _{} _{} 
Table of inner products

























Can you create a similar web page for B_{3}, the wavelet basis for V_{3}?
Web page by Edward Aboufadel, October 2000.