The Haar vector space V2 has dimension 4. One basis for V2 is B2 = {f, y, y1,0,y1,1}. 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 V2
The Haar father wavelet f
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The Haar mother wavelet y
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The Haar daughter wavelet y1,0
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The Haar daughter wavelet y1,1 |
Table of inner products
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Can you create a similar web page for B3, the wavelet basis for V3?
Web page by Edward Aboufadel, October 2000.