Statistical analysis of nonparametric transfer function estimates

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