An Efficient Implementation for Regularized Frequency Response Function and Transient Estimation

In this paper, we propose an efficient implementation for the kernel-based regularized frequency response function (FRF) and transient estimation. In particular, we show that when the diagonal correlated (DC) kernel is used, the output kernel matrix in the frequency domain has a hierarchically of-diagonal low-rank (HODLR) structure, and by exploring this structure, the FRF and transient estimates can be computed very efficiently The overall computational complexity is O ( y 2 N b ) log 2 N b ), where N b is the number of data in the interested frequency band and 7 is the HODLR rank of the output kernel matrix that is often much smaller than N&. The efficacy of the proposed implementation is demonstrated by numerical simulations.