I know the three Haar basis functions
//mother wavelet:
[1 1 -1 -1]
//dilation:
[1 -1 0 0]
//translation:
[0 0 1 -1]
However, the Haar basis consists of four basis elements: The mother wavelet, the translation, the dilation and another, fourth element, which I don't understand. According to this, this fourth element is
[1 1 1 1]
But how would this one look like, and how is it obtained (dilation/translation, whatever combination)? This confuses me.
Btw: is the Haar basis defined as
[ 1 1 1 1
1 1 -1 -1
1 -1 0 0
0 0 1 -1]
or as the transpose of this?