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highest expected or required accuracy of the instrument or compo
nent tested.
The conversion can be expressed symbolically as:
(So -T D„) x: (C, dC) S0 -f- D0.
Cs represents the process of conversion and dC the imperfections oï
it. S0 is the digital equivalent of S0> and if dC is insignificant D0
represents the digital equivalent of D0.
In detective tests the aim of data processing is to separate the
regular and random errors as good as possible, to estimate their
magnitude and to detect their sources. The corresponding accuracies
should also be estimated. The theoretical tools for achieving this
are the mathematical models linking the input, the process with
undesired disturbances, and the output. The choice of the mathe
matical model and the structure of the testing process have been
made according to the same considerations.
The mathematical model, written in general terms, is:
(Si -j- Dt) ijxjPj-f cLP) m (S0 -f- D0) m
input process output
model model model
In the testing of instruments, the input and output models may
be regarded as known. The establishment of the model of the process
with disturbances is a rather delicate problem. The relevant ma
thematical modeling applies to phenomena involved in the flow
of the semantic or/and metric information.
Generally, the mathematical models should fulfil the following
requirements
I) they should be versatile thus applicable to a larger group
of instruments. Specific models should be simplifications of
the general one.
II) they should represent the process and the disturbances
involved sufficiently accurately. The accuracy should be
matched with the expected maximum useful information
contained in the input and output models.
Ill) they should be adapted to the available means and possibili
ties for data processing (e.g. computers).
In the ideal case, where the input and the process (including
conversion) are perfect, there is a simple relation:
Si x Ps S0, or in terms of models: Sim x Psm Som-
For linear or "linearised" processes, this expression can be sub
tracted from the corresponding one, valid for the imperfect case.
