Language as a carrier of information - Signals, Processes, and Systems - page 113

It is important to proceed according to scientific method. First, a number of possibilities
based on an idea which can be explained in physical terms must be considered. They must
be carefully tried out experimentally and reported.
A perfect solution is not possible on this basis, only the best in a relative sense. Our brain
uses additional extremely effective methods, for instance, and recognises the word uttered
from the context. This is where even DASY Lab has its limitations.
Pattern recognition
Basically, in introducing correlation we have taken up the fundamental phenomenon of
communication: pattern recognition. A transmitter cannot communicate with a receiver
unless a store of patterns conveying meaning exists or has been agreed. It doesn't matter
whether it is a technical modulation process or a holiday abroad with its attendant
language problems.
So that you do not have to use the module "correlation" in an uninformed way we will
demonstrate here how straightforward pattern recognition can be (though it is not always
so straightforward!). How is the correlation factor - that is the "similarity of two signals
given as a percentage" - calculated by the computer?
Illustration 85 provides the basis of the explanation. The top half is intended to remind
you that the computer in reality processes strings of figures arithmetically and does not
represent continuous functions. The strings of figures may be represented graphically as
a sequence of measurement data of a certain level.
The correlation factor for the two lower signals is now to be determined. The lower signal
is to be the reference signal. We are not interested in whether it is the frequency or time
domain. For the sake of simplicity we limit the number of measurement data to 16 and
quantize the signal, by allowing only 9 different integer values from 0 to 8.
Now we shall multiply the measurements one below the other by each other. All the
products are then totalled. This results in
2 < 6 + 2 < 7 + 2 < 8 + 3 < 8 + 3 < 8 + 4 < 8 + ......+ 7 < 1 + 7 < 1 + 0 < 7 + 0 < 8 = 273
This figure already says something about the similarity; the greater it is the more
agreement there should be.
But how do we "scale" this value so that it lies between 0 and 1? As the lower signal was
taken as the reference signal the „similarity between the reference signal and itself“ is
determined in the same way. This gives
2 < 2 + 2 < 2 + 2 < 2 + 3 < 3 + 3 < 3 + 4 < 4 + .......+ 7 < 7 + 7 < 7 + 7 < 7 + 8 < 8 = 431
At 431 the agreement would be 100% or 1.0. By dividing the upper by the lower figure
(calculation using rule of three) we obtain 271/431 = 0.63, i.e. a similarity of 63% between
the two signals or signal segments.