Prewhitening Followed by Sampling Versus Sampling Followed by Prewhitening for Detection

Abstract

The detection of known signals in colored Gaussian noise typically involves applying a matched filter to prewhitened data samples in the discrete-time domain. This is achieved by sampling the continuous-time data and applying a prewhitener before applying a matched filter. An alternative approach switches the order of sampling and whitening; whitens the data using an analog prewhitener before sampling. These two methods have been widely regarded as equivalent when sampling at the Nyquist or a higher rate. In this study, we demonstrate that these approaches are indeed equivalent when all Nyquist or higher rate samples are utilized. However, when performing detection using only a subset of the Nyquist samples, the equivalence breaks down. We show that for sparse signal detection, these approaches diverge; the implementation utilizing an analog prewhitener followed by a sampler is both computationally feasible and superior in terms of detection performance.

Keywords

• Autoregressive process
• deflection coefficient
• matched filter
• prewhitening
• signal detection
• sparse samples