A new paradigm established for the investigation of errors in frequency-domain measurements was applied to the phase sensitive detection ͑PSD͒ algorithm used in lock-in amplifiers, one of two techniques commonly used for spectroscopy measurements. For additive errors in time-domain signals, the errors in the phase angle and magnitude were found to be uncorrelated, even when time-domain errors were not normally distributed. In contrast to results obtained using the frequency response analysis

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... orithm, errors in the real and imaginary impedance were found to be correlated, and the variances of the real and imaginary parts of the complex impedance were not equal, except at a phase angle of Ϫ/4. A propagation of error model was established to explain and confirm the calculated statistical properties. The statistical characteristics of the results were in good agreement with experimental observations.