Evolutionary spectrum estimation for uniformly modulated processes with improved boundary performance

The evolutionary spectrum (ES) is a time-dependent analogue of the spectrum of a stationary process. Existing estimators of the ES suffer from bias problems in the boundary region of the time-frequency domain, due to windowing effects. We propose a new estimator of the ES of a uniformly modulated process which mitigates these problems. Our estimator is based on an extrapolation of the ES in time, using an estimate of the time derivative of the ES. We apply our estimator to a simulated example of a uniformly modulated process with known ES.