njit-etd2003-081 - New Jersey Institute of Technology

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are particularly bad in this regard. Dealing with the combination of noise and nonlinearity
requires the understanding of the necessary measurement tradeoffs to assure an
accurate transfer function estimation.
3.13.1.1 Imperfections in Dynamic Systems. Biological control systems typically
have higher noise and less linearity than the typical electrical or purely mechanical
system. The non-linear behavior is often due to the physiological components involved
in the system. The measurement noise is often a result of the system being characterized
under actual operating conditions.
3.13.1.2 Balancing Noise and Non -linearity. To make a transfer function
measurement on a dynamic system, an excitation is supplied to the system and the
system's response to this excitation is measured. If the system is noisy but linear, the
excitation level can be increased to improve the signal to noise ratio by simply
overpowering the noise. If the system is non-linear (for example at high excitation
amplitudes), but noise free, the excitation can be lowered to a point where the linearity is
acceptable.
When the system is both non-linear and noisy, a tradeoff must be made balancing
the poor signal-to-noise ratio at low excitation amplitudes with the non-linear system
behavior at high excitation amplitudes.
There are two possible approaches of transfer function estimation: swept-sine
and a broadband FFT based network analyzer.
The swept sine (or more accurately stepped-sine) estimation technique is the
least affected by noise and non-linear system behavior. The tradeoff with the swept-sine