Adaptive State-Space Multitaper Spectral Estimation

Short-time Fourier transform (STFT) is the most common window-based approach for analyzing the spectrotemporal dynamics of time series. To mitigate the effects of high variance on the spectral estimates due to finite-length, independent STFT windows, state-space multitaper (SSMT) method used a state-space framework to introduce dependency among the spectral estimates. However, the assumed time-invariance of the state-space parameters makes the spectral dynamics difficult to capture when the time series is highly nonstationary. We propose an adaptive SSMT (ASSMT) method as a time-varying extension of SSMT. ASSMT tracks highly nonstationary dynamics by adaptively updating the state parameters and Kalman gains using a heuristic, computationally efficient exponential smoothing technique. In analyses of simulated data and real human electroencephalogram (EEG) recordings, ASSMT showed improved denoising and smoothing properties relative to standard multitaper and SSMT approaches.

Automated summary

Short-time Fourier transform (STFT) is a commonly used method for analyzing the spectrotemporal dynamics of time series, but it has the problem of large estimation errors. To solve this problem, the state-space multitaper (SSMT) method is used. However, this method is difficult to capture the highly nonstationary spectral dynamics of time series. We propose an adaptive SSMT (ASSMT) method, which tracks highly nonstationary dynamics by adaptively updating the state parameters and Kalman gains.