Statistical analysis of nonparametric transfer function estimates

摘要

The Empirical Transfer Function Estimate (ETFE) is the ratio ofthe Fourier transforms of the output and input signals of a system. Itworks well when the input signal is deterministic. However, when theinput signal is random, or it can only be observed with an observationerror, the quality of the ETFE deteriorates. Its variance can beinfinite, even for high signal-to-noise ratio. This is not well known.This paper establishes and analyses a mathematical model of the ETFEwith noisy input signals. It explains the cause of the large variance,and suggests modifications which eliminate the above problems