1. But

Build all or part of an inter-spectral or transfer matrix from functions or a table of functions.

When the user chooses to enter a series of functions, they are used in full. When the user chooses to enter a table_function, the stored functions can be split, averaged and windowed, with a given overlap.

To clarify the point, we assume that the user has 2 functions \(A\) and \(B\). If he chooses to use the operator from functions, the definition of the interspectrum \({G}_{\mathrm{AB}}\) that he will calculate will necessarily be

\({G}_{\mathrm{AB}}=\frac{1}{{N}_{A}}\mathrm{FFT}(A)\ast \mathrm{FFT}{(B)}^{\mathrm{H.}}\).

Where \({N}_{A}\) is the number of points in the \(A\) vector. If he chooses to build a table_function with the functions \(A\) and \(B\), he can extract \(N\) under vectors \({A}_{\mathrm{1,}}\mathrm{...},{A}_{N}\) from the vector \(A\) (resp. \({B}_{\mathrm{1,}}\dots ,{B}_{N}\) from the vector \(B\)), and calculate an averaged interspectrum \({G}_{\mathrm{AB}}\) such that

\({G}_{\mathrm{AB}}=\frac{1}{{N}_{A}}(\frac{1}{N}\sum _{k=1}^{N}\mathrm{FFT}({A}_{k})\ast \mathrm{FFT}{({B}_{k})}^{\mathrm{H.}})\).

The functions read are of the sd_function type.

The product concept is of an interspectrum type.

It is possible to use this operator in a Code_Aster, command file but also interactively using the operator CALC_ESSAI (U4.90.01).