Design of optimum filters for analog feedback telemetry system

An analog feedback telemetry system having noise in both the forward and feedback channels is analyzed. The complete system is treated as a feedback control system with disturbances in forward and feedback loops and technique of calculus of variation is applied to study the optimum performance. Cases of both with and without delay in the channels are considered. The technique evaluates the expressions for optimum filters which minimizes the mean square error between the data sent and the data received. Various cases of correlation between signal and noise processes are considered and expressions of optimum filter-transfer functions are derived. Mean square errors are evaluated for various cases of correlation. It is shown that for the systems where noise in the feedback channel is not correlated either with forward channel noise or the signal, a feedback channel is not required for optimum performance. Channel delays could also be adjusted to minimize the mean square error.