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National Advisory Committee for Aeronautics, Technical Notes - Application of Several Methods for Determining Transfer Functions and Frequency Response on Aircraft from Flight Data

In the process of analyzing the longitudinal frequency—response
characteristics of aircraft, information on some of the methods of analy—
sis has been obtained by the Langley Laboratory of the National Advisory
Committee for Aeronautics. In the investigation of these methods, the
practical applications and limitations Were stressed.

In general, the methods considered.may be classed as: (1) analysis
of sinusoidal response, (2) analysis of transient response as to har-
monic content through determination of the Fourier integral by manual or
machine methods, and (5) analysis of the transient through the use of
least-squares solutions of the coefficients of an assumed equation for
either the transient time response or frequency response (sometimes
referred to as curve—fitting methods).

The investigation has led to the following observations: The curve-
fitting methods (Donegan—Pearson and exponential-approximation methods)
appear to be less critical to inputs having regions of low harmonic con-
tent than Fourier methods and present the frequency response as analyti-
cal expressions (transfer functions). Fourier methods indicate charac-
teristics of frequency response that may be missed in curve—fitting
methods because of the limitations on the assumed form of the equations
used in the curve—fitting methods. For manual calculations, the anegan-
Pearson method appears to be best suited.for highly damped systemsEin
response to arbitrary control inputs, the exponential-approximation
method appears to be best suited for lightly damped systems in response
to step or short-pulse control inputs, and the Fourier method offers
comparable results but requires lengthy calculations. Special machines
for performing the Fourier analysis, such as the Coradi harmonic analyzer
and the Fourier sythesizer, reduce the time required for the solution
but do not offer particular improvement in accuracy over the usual manual
methods. The use of punch—card calculating machines for the evaluation
of the Fourier integrals appears to offer possibilities of more acéurate
results with a large reduction in time over the usual manual methods.