A counterexample on continuous coprime factors

In Georgiou and Smith (1992), the following question was raised: Consider a linear, shift-invariant system on L/sub 2/[0, /spl infin/). Let the graph of the system have Fourier transform (MN)H/sup 2/ (i.e., the system has a transfer function P=N/M) where M, N are elements of C/sub A/={f/spl isin/H/sup /spl infin//: f is continuous on the compactified right-half plane}. Is it possible to normalize M and N (i.e., to ensure |M|/sup 2/+|N|/sup 2/=1) in C/sub A/? The author shows by example that this is not always possible.<
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