Computationally Efficient Synchronous Demodulation using Sigma-Delta Approach

Synchronous detection is an approach used to detect very low level signals within noise when the excitation signal is precisely known or generated locally. In the instrumentation and measurement field, this is generally termed lockin detection and the instrument is a lockin amplifier. A direct implementation samples the measured signal to the required precision, and then applies the lockin algorithm to the data in order to recover an estimate of the measured parameter. The mixing inherent in the lockin requires multiplication as well as filtering. In this paper, we propose dispensing with the full analog to digital conversion prior to analysis. The proposed method operates directly in the digital domain, with both filtering and synchronous averaging performed using oversampled bilevel signals. It is further shown that the required computation can be performed recursively and without the requirement for multiplication. The recursive calculation is exact, and no approximations are involved. This enables lower-complexity hardware and permits operation in resource-constrained devices where arithmetic, especially floating-point, is unavailable.