SNR Degradation in Undersampled Phase Measurement Systems

A wide range of measuring applications rely on phase estimation on sinusoidal signals. These systems, where the estimation is mainly implemented in the digital domain, can generally benefit from the use of undersampling to reduce the digitizer and subsequent digital processing requirements. This may be crucial when the application characteristics necessarily imply a simple and inexpensive sensor. However, practical limitations related to the phase stability of the band-pass filter prior digitization establish restrictions to the reduction of noise bandwidth. Due to this, the undersampling intensity is practically defined by noise aliasing, taking into account the amount of signal-to-noise ratio (SNR) reduction caused by it considering the application accuracy requirements. This work analyzes the relationship between undersampling frequency and SNR reduction, conditioned by the stability requirements of the filter that defines the noise bandwidth before digitization. The effect of undersampling is quantified in a practical situation where phase differences are measured by in-phase and quadrature (I/Q) demodulation for an infrared ranging application.