A. Appendix

1.

Let us assume that there exists no error and that the estimated superimposing structure f₀ represents the real main structure f in order to be able to estimate the ranges of the function G.

The estimated amplitude has the following form:

The restriction p>-q has the following explanation:

but the estimated amplitude has to be larger than zero. G(x) has the following form:

Assume that the following holds:

This inequation cannot be fulfilled due to the restriction in Eq. (2 (click here)).

2.

The upper boundary of G depends on the ratio between the main structure hf(x) and the substructures . If the ratio and , the following estimations hold:

The first estimation is easy to prove:

If , e.g.

If , the values of G run away, but this happens only in case of an extremely underestimated amplitude. The case is impossible because the amplitude has always to be larger than zero.

It is only possible to estimate the value of L. If the main component superimposes for example the substructures, the ratio between the main structure and the underlying substructures has to be less than one. Therefore .

3.

Let us assume that there exists no error and that the estimated superimposing structure f₀ represents the real main structure f in order to be able to estimate the ranges of the function G.

If the estimated amplitude converges to the real amplitude h, the following estimation can be done:

 

Equation (9 (click here)) has to be larger than or equal to zero because of condition 2 (click here). Due to the assumption that , the equation is less than 1. The more the main structure superimposes the substructures, the lower the value of G has to be.