Digital Signal Processing Reference
In-Depth Information
Mathematical model of the electrical conductor resistance R
l
A
ρ
R =
l : = length of conductor (in m);
A := cross section (in mm
2
);
ρ
mm
2
/m)
:= specific resistance of the material(in
Ω
ρ
Note: the model is limited to three variables(
, l, A). Thus the minimal influence of the temperature of
the conductor on electrical resistance R is left out of accoun. The model is valid for20°
.
The model guarantees …
•
Precision
: any combination of specific values for
, l and A produces an exact result
which only depends on the accuracy of measurement of the quantities given .
ρ
•
Lack of ambiguity
: any combination of numbers of
ρ
, l and A describes a discrete
physical situation and produces a single result for R .
•
Simplification
: the mathematical model describes the method of calculation of the
electrical resistance of the conductor for an infinite variety of different materials , lengths
and cross -sections.
•
Communicability
: the mathematical model is valid irrespective of language or other
barriers , i.e. worldwide
•
Verifiability
: the mathematical model is experimentally verifiable . Innumerable
measurements with the most varied of materials , lengths and cross -sections confirm
without exception the validity of the model .
•
Predictability
: the conductor resistance for a given material , length and cross -section
can be predicted . In the case of a short -circuit it is possible by measuring the conductor
resistance in a cable to predict where the defect is located provided the material and the
cross-section are known and the conductor has a homogeneous structure .
•
Lack of redundancy
: the mathematical model does not contain any "padding ", it
produces pure information .
Note
:
mathematical models in physics are not provable in the sense of strict mathematical
logic. Here the tenet -"the experiment (meaning experimental verification ) - is the sole arbiter
of scientific truth" - is applicable.
Illustration 11:
Features of mathematical models demonstrated by means of a simple example.
In search of other "tools"
The "theory of signals, processes and systems" is understood as the creation of mathema-
tical models of signal technology processes on the basis of physical oscillation and wave
phenomena and quantum physics (still not completely understood). This applies against
the background that
nothing
works in technology that contravenes natural laws. All the
framework conditions and explanatory models in technology must therefore inevitably
derive from natural laws, and more specifically from physics.
