To pass from the temporal signal to
its frequential components is a difficult mathematical spot. For that, we use
the Fourier transform. Our current computational tool is well on the
computer. This tool is powerful, but limited at the same time.
Our temporal signal is analogical. It contains an infinity of values. The variable t belongs to set
of positive real values. It is for this reason, mathematics thus physical, that we
can represent a signal with a continuous curve ;
We visualize a current of
interference above 2 000 Hz + 2 100 Hz, of period 20 ms (1/2 period is posted).
So that signal can be recorded on the computer, we will digitize it. We sample
the signal with an interval allowing to reproduce the signal of origin
accurately. The number of samples is here of 1024 points.
It is then necessary to apply the *discrete*
Fourier transform to visualize the signal in the frequential
plan. This transform is conceived for the sampled signals. We already know by
advance, that the interference current, is composed of carrying medium
frequency and a interference frequency of low frequency . This low frequency is
in the beginning, partly, of the properties which we grant to this type of
current.
Science does not seem agreement with
our theories. We allot low frequency properties to a current which does not
contain any.
Is mathematics therefore, counters
us ?
The trigonometrical formula to use
is known, but once again, we are deceived by our perceptions. If it is true the
left member of equation contains well a addition operand and our starting
values 2 000 and 2 100 Hz, it is not the same for the right term. The right
member contains well the values of 2 050 and 50 Hz, but in a combined form. It
is not possible to see the following formula there ;
Our bad knowledge of physics and
mathematics is responsible for beliefs, resting on no truth scientists.
