Figure 9—NPO run number 6
We have obtained a complete description of the NPO which involves 74 formulas. These treat the noise in the various outputs, invariances of the NPO and other interesting features. A presentation of these would be outside of the scope of this paper and would tend to obscure the main features of the NPO. Thus, we show here only a typical sample of the computer simulation, [Figure 8] and [Figure 9]. Conditions for these runs are shown in [Table I]. Run No. 6 duplicates run No. 5 except for the fact that i₁ and i₂ were disabled in run No. 6.
Observe that all our descriptions of the NPO and the space it is to decompose have been time invariant while the signals shown in the simulation are presented as functions of time. The conversion may be effected as follows: Given a measurable (single-valued) function
x = x(t)t ∊ T
where
μ(T) > 0
we define the space
X = {x = x(t) ∍ t ∊ T}
and a probability distribution
| μ(x⁻¹(X′)) | ||
| P(X′) = | ———— | X′ open ⊂ X |
| μ(T) | ||