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Figure 2. Function, characterizing "scattering" 
properties of neurons 
Utilization of different spheres enables to 
establish group of parameters which suffered 
influence of external signal. This parametrization 
is very useful for building of two dimensional 
network. The number of them may be chosen basing on 
model of sphere (number of its layers and indices). 
Function Q (x) in itself is of no importance but 
analizing ; ; 
y - ve =0 
we can obtain all discrete spectrum components 
corresponding to y(x). V (x) is obtained by similar 
steps (only direction of wave is opposite).Accuracy 
of this method depends on a number of tests with 
random trajectory of photons. 
Numerical experiment has demonstrated that those 
signals which have more narrow Fourier spectrum have 
as well more poor spectrum of descrete components.It 
was suggested constancy of amplitude during 
comparison. In other words the more number of 
components in the sum the more width of Fourier 
spectrum for optical signal.Thus analysis shows one- 
to-one correspondence between amplitude spectrum of 
signal and its descrete one. 
It should be note that for producing ordinal 
Fourier transform it is neecessary to carry out 
several mathematical operations, as a rule using 
analog to digit transform. Details of this theory 
are well known. 
It fulfils program realization of signal proces- 
ing. And descrete-analog network carries out 
apparatus spectral transform. 
2.3 Signal spectrum 
Before formulation of principles for networks 
with nonlinear interconnections it is necessary to 
make theoretical discussion of experimentally recei- 
ved results.It is convenient to consider rectangular 
distribution of illuminance at the detector 
plane.The method of finding of discrete spectrum for 
different signals one can find in /8/.Let's define 
arbitrary distribution as a limit of sets of 
rectangulars when there widths are small enough 
(see Fig.3). 
Then koefficients a(k) and b(k) are 
li, gy Lei. TE: EY o Ee ge x. + 
(6) ZA Lye i e t1) *«] 
  
  
  
  
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN 
Fiqure 3.Discrete representation of initial 
conditions at the detector plane 
- E -L$9t. -L(i-&)mT 
uit Q8 Xe e £)*, | 
SEE ME) tte its das 
where ES Lt ay 
expression 
$n- 
An = 4 [An (+ p 
X. ns 
Peis (=e ing, pe 9e eem 
and we have as well recurrent 
je I$ 4 ^ D i i e ES ates 
This recurrence enables to obtain general formula 
for afk) and estimate influence of high frequency 
part of spectrum on discrete components of spectrum. 
General form of alk) is obtained from (6) and 
(7) .That is $ 
-W-L nd 
a(k) =À € eral] Gif n PE tonte To! 
+ g, 1! i= , (14° St £ an ca) npo Z., e 
where A s 5; are sign functions. E de e 
we get 
p E 1 (Les; $n ) 
i ini s expi 2 (A, sourds 30) 
3. P (reg; EM Em ^ 
n-i+l . 
- P —-1ko : 
at z X EE KK 2) = t e «(t d, 
In other words the left part of (8) defines 
components of following type 
€——— 
(8) L*S: des =4+S; TE Ais. 
t V^ n-ı +4 ks t m-i+s 
where Ay,.;- increment of y,. 
I£ the first derivative of y with respect tox 
is small within space of existence of illuminance at 
the detector plane or in other words the real object 
has not bright points or lines, then 
à dns — O 
Kê+ 45 -*£ 
Solution of (8) defines only Al and Bl.Those objects 
are equivalent to light source with the rectangular 
boundaries of brightness at the detector plane. But 
it’s not means that middle and high part of spectrum 
have not any correspondence with discrete components 
of nonlinear spectrum. Weak change of illuminance 
defines collection of solitons with low amplitudes 
and small velocities. Using theory of amplitude 
spectral analysis to pick out some part of spectrum 
it is necessary to build optical system with great 
accuracy. With the aid of neuron networks this task 
can be solved significantly easyer without analog to 
digit transform. 
19