Coherence Expectation Minimisation and Combining Weighted Multitaper Estimates

Coherence is a useful measure in many engineering applications. Here, we focus on the case where the input signal to a linear system can be measured free from noise, but the output signal is perturbed by noise. A novel expression for the expectation of a multitaper magnitude squared coherence estimate for this case is presented and verified through numerical evaluation. Additionally, the expression is used to optimise a multitaper coherence estimation method, which gives improved coherence estimation in detection. A clever combination of two weighted magnitude squared coherence multitaper estimators yields a new method, called Combined Weighted Multitaper Coherence (CWMC). The method is evaluated and compared to the Thomson multitaper method for simulated data and on real visual evoked potential electroencephalogram data, showing consistent improvement using CWMC.