An adaptive multi-taper spectral estimation for stationary processes

Abstract

The multi-taper spectral estimation method is effective in reducing both bias and variance of the spectrum of stationary stochastic processes. The number of tapers (NoT) in the method controls the bias and variance trade-off of the spectrum. In general, the NoT is empirically determined and constant at all frequencies, limiting the adjustment of the local bias and variance. This paper develops an adaptive multi-taper approach with the varying NoT at each frequency point for estimating the power spectral density (PSD) and coherence function of multivariate stationary processes. An iterative procedure with a stopping criterion is proposed to optimize the NoT at each frequency without manual tunning. The sine taper with a simple analytical expression and satisfactory leakage protection is employed. The proposed adaptive multi-taper approach is applied to three numerical examples, the structural response of a building model, a wind speed process, and an autoregressive process, which exhibit different spectral characteristics. The results of all examples show that the proposed approach outperforms Welch’s and traditional multi-taper methods in estimating the PSD and coherence with a smaller bias and variance.