Biomedical Engineering Reference
In-Depth Information
CHAPTER
17
Transfer Function Via
Spectral Analysis
17.1 INTRODUCTION
This chapter describes the method for estimation of the frequency response of a lin-
ear system, using spectral density functions. The autocorrelation and cross-correlation
functions are discussed to provide background for the development of their frequency
domain counterparts, the autospectral and cross-spectral density functions. The coher-
ence function is also discussed as a means of calculating the error in the transfer function
estimation. Applications will be restricted to single input/single output models, where it
is assumed that systems are constant-parameter, linear types.
To meet control system specifications, a designer needs to know the time response
of the controlled variable in the system. Deriving and solving the differential equations
of the system can obtain an accurate description of the system's response characteristics;
however, this method is not particularly practical for anything but very simple systems.
With this solution, it is very difficult to go back and decide what parameters need to be
adjusted if the performance specifications are not met. For this reason, the engineer would
like to be able to predict the performance of the system without solving its associated
differential equations and he/she would like for his/her analysis to show which parameters
need to be adjusted or altered in order to meet the desired performance characteristics.
The transfer function defines the operation of a linear system and can be expressed
as the ratio of the output variable to the input variable as shown in Fig. 17.1.
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