A sampling theorem is presented which is valid for the negative-exponentially correlated output of lock-in amplifiers, electrooptic devices, and electronic circuits in general. A closed-form analytic expression is derived that gives the reduction in the standard deviation of the mean for any sampling interval and any number of samples N. In the limit of independent samples it approaches 1/√N, as expected. The optimum sampling rate is shown to be faster than the Nyquist rate. The sampling rate should be at least one sample per time constant and at this rate the improvement in signal-to-noise ratio (SNR) is approximately √N/2. The maximum improvement in SNR due to signal averaging is shown to be proportional to the square root of the time allotted to take the data.
© 1989 Optical Society of America
Steven J. Wein, "Sampling theorem for the negative exponentially correlated output of lock-in amplifiers," Appl. Opt. 28, 4453-4457 (1989)