My solution to this problem is posted on the Web site.

Although most people did fine on this homework, very few (well, one actually) got full credit. For full credit, I wanted to see a proper explanation of what the system was doing (namely, converting TDM data to FDM and back again), and I demanded matrix notation in your algebra. The reason for this is that it greatly simplifies things, saving unnecessary algebra. It also gives great insight into what is going on.

The perfect reconstruction property caused a little trouble. It is necessary to force PR by choosing an appropriate function for G(z). It does not happen by itself. Furthermore, the choice to achieve PR in the notes (for filter banks) is not the choice for this system, as it leads to gain, which breaks the PR condition. Don't just blindly apply results from the notes without thinking about it!

Tom