The following page gives a definition of perfect reconstruction filter banks (This is actually an extract of my wavelet tutorial, so following the links will lead you out of the Matlab Tutorial).

The essential scheme is the following:

We have perfect reconstruction filter banks if the output of the diagram is the same as the input. The purpose of this tutorial is not to build such filters; indeed, much work has been done to design these filter banks, and we can simply tap into the internet to get the filters.
What we will is implement the various boxes in diagram, and then use them recursively to implement the discrete wavelet transform, and experiment with it.
More precisely, we will implement the following operations

• Convolution (this corresponds to the boxes with letters in it; actually they are linear time invariant filters).
• Downsampling (the boxes with a down arrow)
• Oversampling (the boxes with an up arrow)
• Summation of signals (the plus sign at the right)