TABLE OF CONTENTS Many methods for data analysis and modeling can be formulated in the frequency domain. Frequency domain analysis has certain advantages, including physical insight in terms of frequency content, direct applicability to control system design, and a smaller number of data points for parameter estimation, among others. The basis for frequency domain methods is the finite Fourier transform, which is the mechanism for transforming time-domain data to the frequency domain. Any errors in the transformation from time to frequency domain affect the accuracy of the data in the frequency domain, which in turn impacts data analysis and modeling results. This chapter begins by presenting a method for accurately evaluating the finite Fourier transform for sampled time-domain data, and continues with a discussion of spectral densities and frequency response computed from measured input-output data.
For parametric modeling in the frequency domain, two different models for uncertainty are considered, the Fisher model and the Least Squares model. The Bayesian model is not discussed because of difficulties in formulating probability densities for complex random variables, and the consequent very limited use of this model in aircraft parameter estimation. The two models for frequency domain analysis have the following forms:
Fisher Model:
? is a vector of unknown constant real parameters.
is a complex random vector with probability density p( ).
Least-Squares Model:
? is a vector of unknown constant real parameters.
is a complex random vector of measurement noise.
In the measurement equations, 
( ?) is a...
