This appendix includes the calculations of the probability density functions and the moments of the total field and power variables. By total variables, we mean the fields or the powers measured by probes or antennas, which simultaneously collects the three Ex, Ey, Ez complex field projections.
The total field variable taking Et as a notation is given by the square root of the sum of six terms made up of all the square complex components of each Ex y zprojection i.e.:
The normalized variable of the total field is designated for the occasion by the lower case et notation. This variable comes from the extension of the definition introduced in section 3.2.3:
We find in this formula the standard deviation σν, which is attached to the complex components of Ex y z.
Knowing that the Ex y z variables all follow the normal probability distribution,the square amplitude of the normalized total et field will be the χ2 variable with six degrees of freedom:
We can thus add to this variable, the pdf of χ2, which is expressed by the notation conventions of ...