Sampling, quantization and computational aspects of the quadrature lock-in amplifier

The phase-sensitive or “lock-in” amplifier is a fundamental tool in experimental physics, and is able to extract exceedingly small signals in the presence of noise. The lock-in operates on the principle of synchronous excitation of the system under test, which effectively moves the desired system response above the influence of 1//f noise. The purpose of the paper is twofold: (i) to investigate the numerical aspects of implementation of the lock-in signal processing, particularly for computationally resource-constrained environments; and (ii) to investigate the tradeoff between A/D resolution and oversampling rates in this particular application, where a synchronous reference signal is available. We conclude that the quantization, sampling rate, and numerical precision aspects are somewhat interrelated when the best possible performance in terms of noise rejection is required.