Convergence in synchronous measurements

Synchronous detection using phase-quadrature reference signals is widely employed as a demodulation technique in communication systems. It also finds application in sensitive measurement systems, where the goal is to estimate the gain of an unknown system which is excited by a sinusoidal or square waveform. In measurement systems, longer integration times are the necessary tradeoff for accuracy in very poor signal-to-noise environments. As a result, is difficult to determine when the measurement has stabilized. This paper proposes a novel convergence estimator which yields an asymptotic estimate of relative error. This paper motivates the need for a convergence test and presents an algorithm to address the problem. Simulation results are used to verify the underlying concepts, and experimental results using real measurements are given to show the applicability of the technique.