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

Most folks had no trouble at all with this problem. Apart from the occasional careless mistake, I had nothing to complain about. Those who wrote non-causal expressions for the first part got a `causality?' comment from me, but didn't lose any points because the problem statement didn't specify that the filter had to be causal. (The same goes for complex coefficients.) Mysteriously, a few people had a factor of z^-2 in the denominator, as if hiding it down there and making it negative somehow removed the stigma of non-causality; please don't do this, as it's completely unorthodox and difficult to read.

The second part is correctly tackled by working forwards from the expression for the analog prototype, not backwards from the expected digital filter. It's a simple matter of matching up powers of z.

Tom