In the context of linear quadratic Gaussian (LQG) controller design for single-input, single-output, discrete-time, linear, time-invariant systems, a duality is demonstrated between the Kalman filter design phase and the linear quadratic (LQ) design phase, Furthermore, an asymptotic recovery design procedure is proposed. Through specific Kalman filter design choices, the LQG open-loop transfer Function is forced to approach the LQ open-loop transfer function.