The purpose of calibration is in most cases to obtain the parameters of an analytic representation of the transfer function. Assuming that its mathematical form is known, the task is to determine its parameters from an experiment in which the input and the output signals are compared. Since only a signal that has been digitally recorded is known with some accuracy, both the input and the output signals should be recorded with a digital recorder. In comparison with other methods where a predetermined input signal is used and only the output signal is recorded, recording both signals has the additional advantage of eliminating the transfer function of the recorder from the analysis.
Calibration is a classical inverse problem that can be solved with standard least-squares methods.
The purpose of filter 2 is explained below. Storage and retrieval of the data are omitted from the figure. The approximation of a rational transfer function with a discrete filtering algorithm is not trivial. Signals from a typical calibration experiment are shown in Fig. When the transfer function has been correctly parametrized and the inversion has converged, then the residual error consists mainly of noise, drift, and nonlinear distortions.